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MECHANICAL DRAWING, 

ELEMENTARY AND ADVANCED. 



BY 

JOHN S. REID, 

Instructor in Mechanical Drawing and Designing, 
Armour Institute of Technology. 



FOURTH EDITION, REVISED AND ENLARGED. 
FIRST THOUSAND. 



NEW YORK. 

JOHN WILEY & SONS. 

London : CHAPMAN & HALL, Limited. 
1910 



T^ 3 



Copyright, 1898, 1908, 1910, 

BY 

JOHN S. RE ID. 



THE SCIENTIFIC PRESS 

ROBERT DRUMMOND AND COMPANY 

BROOKLYN, N. Y. 



A2732C4 



PREFACE TO THE FOURTH EDITION. 



The third edition of " A Course in Mechanical Drawing " 
was enlarged and improved by the addition of a set of concrete 
problems, "A Course in Lettering " and "Present Practice in 
Drafting Room Methods." 

In this, the fourth edition, the work has been further enlarged 
and improved by adding courses in Advanced Mechanical Draw- 
ing consisting of short elementary courses in Advanced jsomet- 
rical Drawing, Architectural Drawing, Sheet Metal Drafting, 
Machine Details, and Working Drawings made from freehand 
sketches of small machine parts. 

This arrangement will preclude the necessity of using several 
text-books in high schools, manual-training high schools, univer- 
sity preparatory schools, technical colleges, and evening classes 
where a variety of courses are given to meet the needs of students 
preparing for different trades and professions. 

With the addition of these new courses in advanced work it 
has been thought desirable to change the title of the book from 
"A Course in Mechanical Drawing " to " Mechanical Drawing, 
Elementary and Advanced." 

It was very gratifying to the writer to learn that the improve- 
ments in the third edition were well received by both teachers 
and students and it is hoped that the additions to the /fourth 
edition will meet with a like approval. 

John S. Reid. 



PREFACE TO THE THIRD EDITION. 



To meet the demands of high schools, manual training high 
schools, university preparatory schools, technical colleges, and 
evening classes, it has been found necessary to add to "A Course 
in Mechanical Drawing" a concrete set of problems covering the 
full requirements in mechanical drawing for entrance to the more 
advanced classes in machine drawing, elementary machine de- 
sign, and architectural drawing. The minimum time allowed 
in a definite number of working hours for the finishing of each 
plate, as introduced in this edition, is a new feature, and will be 
much appreciated by Instructors when determining the amount 
of work to require from their students in a given term. The 
time allowed for the different plates has been carefully deter- 
mined by taking note of the actual number of hours taken by 
large numbers of students working on the same plates, under the 
same conditions, and a conservative average taken, so that any 
young man of fair intelligence and with an honest endeavor may 
finish any of the plates in the time given. 

The Course in Lettering, which has also been added to this 
edition, will be found to be of great practical benefit to students 
in all kinds of engineering drafting, and will be seen to embrace 



vi PREFACE. 

the most approved practice in drafting room methods at the 
present time. 

The report on the "Present Practice in Drafting Room 
Methods," which will be found at the end of the book, is also 
new, and will interest Instructors and enable them to adopt a 
system in their drawing courses that may closely approximate the 
best practice in the leading and most progressive drafting rooms 
in the United States. 

The thanks of the author are due and are most cordially 

extended to those who have used this book in the past and have 

encouraged and ass : isted him by gracious words and timely 

suggestions. 

John S. Reid. 

Armour Institute of Technology. 
Chicago, 111., September, 1908. 



PREFACE. 



In the course of a large experience as an instructor in 
drawing and designing, the author of this work has often been 
called upon to teach the elements of mechanical drawing to 
students in marine, electrical, railway, and mechanical engi- 
neering. Having tried and failed to find a book on the sub- 
ject that was entirely suitable for his use as a text-book, he 
has found it necessary to prepare the present work. 

This course contains, in the author's judgment, a com- 
plete and concise statement, accompanied by examples, of 
the essential principles of mechanical drawing — all that any 
young man of ordinary intelligence needs to master, by care- 
ful study, the more advanced problems met with in machine 
construction and design. Such works as the author has tried, 
although most excellent from certain standpoints, were either 
incomplete in some of the divisions of the subject or too volu- 
minous and elementary in the treatment of details. 

The author does not imagine this work is perfect, but he 
believes that it comes nearer what is needed in teaching the 
elements of mechanical drawing in technical schools, high 
schools, evening drawing schools, and colleges than any work 
he has examined. 

The chapter on Conventions will be appreciated by students 



Vlii PREFA CE. 

when called upon to execute working drawings in practical 

work. The methods described are considered by the author 

to be those which have met with general approval by the 

experienced American draftsmen of the present time. 

My acknowledgments are due to E. C. Cleaves, professor 

of drawing, Sibley College, Cornell University, for reading 

the manuscript and making some valuable suggestions. 

The Author. 

April i, 1898. 



CONTENTS 



INTRODUCTION. 

PAGE 

The Complete Outfit, Illustrated i 

CHAPTER I. 

Instruments 7 

Use of Instruments 7 

Pencil 7 

Drawing Pen g 

Triangles n 

T Square n 

Drawing Board 11 

Sibley College Scale 12 

Scale Guard 12 

Compasses 13 

Dividers or Spacers 13 

Spring Bows 14 

Irregular Curves 14 

Protractor 14 

CHAPTER II. 

Geometrical Drawing 16 

CHAPTER III. 

Conventions 56 

CHAPTER IV. 

Lettering and Figuring 64 

ix 



X CONTENTS. 

CHAPTER V. 

Orthographic Projection 74 

Shade Lines, Shades, and Shadows 103 

Conventions 104 

Shades ic6 

Shadows 1 1 1 

Isometrical Drawing 122 

Working Drawings ' 129 

Problems in Mechanical Drawing (Course I) „ 135 



CHAPTER VI. 
Architectural Drawing z ^ 2 

CHAPTER VII. 
Architectural Design I 75 

CHAPTER VIII. 
Sheet Metal Pattern Drafting 216 

CHAPTER IX. 

Elementary Machine Details, Including Screws, Nuts, Bolts, Keys, 

Cotters and Gibs, Coupling Springs, etc 228 

Problems in Mechanical Drawing (Course II) 277 

Present Practice in Drafting Room Conventions and Methods in 

Making Practical Working Drawings 289 



MECHANICAL DRAWING. 



INTRODUCTION. 

A NEED has been felt by instructors and students, especially 
in technical courses, for a text-book that would illustrate the 
fundamental principles of mechanical drawing in such a prac- 
tical, lucid, direct and progressive way as to enable the 
instructor to teach, and the student to acquire, the greatest 
number of the essential principles involved, and the ability to 
apply them, in a draftsman-like manner, in the shortest space 
of time. 

With this in mind, the present work has been prepared 
from the experience of the writer, a practical draftsman and 
teacher for over fifteen years. 

THE COMPLETE OUTFIT. 

The outfit for students in mechanical and machine drawing 
is as follows : 

(i) The Drawing-board for academy and freshman work is 
i6"X2i"x£", the same as that used for free-hand drawing. 
The material should be soft pine and constructed as shown by 
Fig. i. 

(2) 1 Scribbling Pencil with rubber tip. 



MECHANICAL DRAWING. 



(3) Pencils, one 6H and one 4H Koh-i-noor or Faber. 

(4) The T-Square; a plain pearwood T-square with a fixed 
head is all that is necessary. Length 21". 




Fig. i. 



(5) Instruments. " Pocket Book" Set, shown by Fig. 2, 
recommended as a first-class medium-priced set of instruments. 
It contains 




Fig. 2. 



A Compass, 5}" long, with fixed needle-point, pencil, pen 
and lengthening bar; a Spring Bow Pencil, 3" long; a 
Spring Bow Pen, 3" long; a Spring Bow Spacer, 3" long; 



INTRODUCTION. 



2 Drawing-pens, medium and small, i Hair-spring Divider* 
5" long; a nickel-plated box with leads. 




Fig. 




Fig. 4. 




(6) A Triangular Boxwood Scale graduated as follows: 
4" and 2", 3" and ij", 1" and J", f" and f", A" and A". 

(7) 1 Triangle 3o°x6o°, celluloid, 10" long. Fig. 4. 



1 " 45°, " 7" " 



MECHA NIC A L DRA WING. 



(8) i Irregular Curve. No. 13. Fig. 5. 

(9) Emery Pencil Pointer. 

(10) Ink, black waterproof. Fig. 7. 

(11) Ink Eraser, Faber's Typewriter. No. 104. 

(12) Pencil Eraser, "Emerald" No. 211. Fig. 9. 








Fig. 



Figs. 10, ii, 



Fig. 7. Fig. 8. 

(13) Sponge Rubber or Cube of "Artgum." 

(14) Tacks, a small carton of 1 oz. copper tacks, and 1 doz. 
small thumb tacks. 



1 " 



(15) Arkansas Oil Stone. 2 /, Xi // XrV 

(16) Protractor, German silver, about 5" diam. 

(17) Scale Guard, " ". Fig. 13. 



Fig. 12, 



INTRODUCTION. 

(18) 2 sheets of " Cream" Drawing Paper. [5"X2o'\ 
(iq) 2 " " Imperial Tracing Cloth. i$"X2q" 

(20) 1 Cross-section Pad. 8"Xio". 

(21) 1 Scribbling Pad. 



y§l|§§^ 



Fig. 10. 




Fig. 11. 




Fig. 12 



(22) i Erasing Shield, nickel plated. 

(23) 2 Lettering Pens, "Gillott" No. 303. 

(24) 2 " " "Ball Point," No. 506. 

(25) 2 " " " " No. 516. 

(26) 1 Two-foot Rule. 



CHAPTER I. 
INSTRUMENTS. 

It is a common belief among students that any kind of 
cheap instrument will do with which to learn mechanical 
drawing, and not until they have acquired the proper use of 
the instruments should they spend money in buying a first- 
class set. This is one of the greatest mistakes that can be 
made. Many a student has been discouraged and disgusted 
because, try as he would, he could not make a good drawing, 
using a set of instruments with which it would be difficult for 
even an experienced draftsman to make a creditable showing. 

If it is necessary to economize in this direction it is better 
and easier to get along with a fewer number, and have them 
of the best, than \t is to have an elaborate outfit of question- 
able quality. 

The instruments shown in Fig. 2 are well made of a moderate 
price, and with care and attention will give good satisfaction for 
a long time. 

USE OF INSTRUMENTS. 

The Pencil. — Designs of all kinds are usually worked out 

in pencil first, and if to be finished and kept they are inked in 

and sometimes colored and shaded ; but if the drawing is only 

to be finished in pencil, then all the lines except construction, 

center, and dimension lines should be made broad and dark, 

6 



INSTRUMENTS. 7 

so that the drawing will stand out clear and distinct. It will 
be noticed that this calls for two kinds of pencil-lines, the 
first a thin, even line made with a hard, fine-grained lead- 
pencil, not less than 6H (either Koh-i-noor or Faber's), and 
sharpened to a knife-edge in the following manner: The lead 
should be carefully bared of the wood with a knife for about 
\ n ', and the wood neatly tapered back from that point ; then 
lay the lead upon the emery-paper sharpener illustrated in the 
outfit, and carefully rub to and fro until the pencil assumes a 
long taper from the wood to the point ; now turn it over and 
do the same with the other side, using toward the last a 
slightly oscillating motion on both sides until the point has 
assumed a sharp, thin, knife-edge endwise and an elliptical 
contour the other way. 

This point should then be polished on a piece of scrap 
drawing-paper until the rough burr left by the emery-papei is 
removed, leaving a smooth, keen, ideal pencil-point for draw- 
ing straight lines. 

With such a point but little pressure is required in the 
hands of the draftsman to draw the most desirable line, one 
that can be easily erased when necessary and inked in to 
much better advantage than if the line had been made with a 
blunt point, because, when the pencil-point is blunt the incli- 
nation is to press hard upon it when drawing a line. This 
forms a groove in the paper which makes it very difficult to 
draw an even inked line. 

The second kind of a pencil-line is the broad line, as 
explained above ; it should be drawn with a somewhat softer 
pencil, say 4H, and a thicker point. 

All lines not necessary to explain the drawing should be 



8 



MECHA NIC A L DRA WI NG . 



erased before inking or broadening the pencil-lines, so as to 
make a minimum of erasing and cleaning after the drawing is 
finished. 

When drawing pencil-lines, the pencil should be held in a 
plane passing through the edge of the T-square perpen- 
dicular to the plane of the paper and making an angle with 
the plane of the paper equal to about 6o°. 

Lines should always be drawn from left to right. A soft 
conical-pointed pencil should be used for lettering, figuring, 
and all free-hand work. 

The Draiving-pen. — The best form, in the writer's opinion, 
is that shown in Fig. 14. The spring on the upper blade 




Fig. 14. 




Fig. 15. 

spreads the blades sufficiently apart to allow for thorough 
cleaning and sharpening. The hinged blade is therefore 
unnecessary. The pen should be held in a plane passing 
through the edge of the T-square at right angles to the plane 
of the paper, and making an angle with the plane of the 
paper ranging from 6o° to 90 . 



INSTRUMENTS. 9 

The best of drawing-pens will in time wear dull on the 
point, and until the student has learned from a competent 
teacher how to sharpen his pens it would be better to have 
them sharpened by the manufacturer. 

It is difficult to explain the method of sharpening a draw- 
ing-pen. 

If one blade has worn shorter than the other, the blades 
should be brought together by means of the thumb-screw, and 
placing the pen in an upright position draw the point to and 
fro on the oil-stone in a plane perpendicular to it, raising and 
lowering the handle of the pen at the same time, to give the 
proper curve to the point. The Arkansas oil-stones (No. 15 
of " The Complete Outfit ") are best for this purpose. 

The blades should next be opened slightly, and holding 
the pen in the right hand in a nearly horizontal position, place 
the lower blade on the stone and move it quickly to and fro, 
slightly turning the pen with the fingers and elevating the 
handle a little at the end of each stroke. Having ground the 
lower blade a little, turn the pen completely over and grind 
the upper blade in a similar manner for about the same length 
of time ; then clean the blades and examine the extreme 
points, and if there are still bright spots to be seen continue 
the grinding until they entirely disappear, and finish the 
sharpening by polishing on a piece of smooth leather. 

The blades should not be too sharp, or they will cut the 
paper. The grinding should be continued only as long as the 
bright spots show on the points of the blades. 

When inking, the pen should be held- in about the same 
position as described for holding the pencil. Many drafts- 
men hold the pen vertically. The position may be varied 



10 MECHANICAL DRAWING. 

with good results as the pen wears. Lines made with the pen 
should only be drawn from left to right. 

THE TRIANGLES. 

The triangles shown at Fig. 4 (in il The Complete Outfit ") 
are 10" and j" long respectively, and are made of transparent 
celluloid. The black rubber triangles sometimes used are but 
very little cheaper (about 10 cents) and soon become dirty 
when in use; the rubber is brittle and more easily broken than 
the celluloid. 

Angles of 15 , 75 , 30 , 45 , 6o°, and 90 can readily be 
drawn with the triangles and T-square. Lines parallel to 
oblique lines on the drawing can be drawn with the triangles 
by placing the edge representing the height of one of them 
so as to coincide with the given line, then place the edge rep- 
resenting the hypotenuse of the other against the corre- 
sponding edge of the first, and by sliding the upper on the 
lower when holding the lower firmly with the left hand any 
number of lines may be drawn parallel to the given line. 

The methods of drawing perpendicular lines and making 
angles with other lines within the scope of the triangles and T- 
square are so evident that further explanation is unnecessary. 

THE T-SQUARE. 
The use of the T-square is very simple, and is accom- 
plished by holding the head firmly with the left hand against 
the left-hand end of the drawing-board, leaving the right 
hand free to use the pen or pencil in drawing the required 
lines. 



INSTRUMENTS. II 

THE £>RAWING-BOARD. 
If the left-hand edge of the drawing-board is straight and 
rven and the paper is tacked down square with that edge and 
Ihe T-square, then horizontal lines parallel to the upper edge 
of the paper and perpendicular to the left-hand edge may be 
drawn with the T-square, and lines perpendicular to these 
can be made by means of the triangles, or set squares, as they 
are sometimes called. 

THE TRIANGULAR SCALE. 

This scale, illustrated in Fig. 3 (in "The Complete Out- 
fit"), was arranged to suit the needs of the students in machine 
drawing, It is triangular and made of boxwood. The six 
edges are graduated as follows; T V' or full size, z \ f/ , f" 
and f" = 1 ft., 1" and \" = 1 ft., 3" and \\" = I ft., and 
4" and 2" = 1 ft. 

Drawings of very small objects are generally shown en- 
larged — e.g., if it is determined to make a drawing twice the 
full size of an object, then where the object measures one inch 
the drawing would be made 2" ', etc. 

Larger objects or small machine parts are often drawn full 
size — i.e., the same size as the object really is — and the draw- 
ing is said to be made to the scale of full size. 

Large machines and large details are usually made to a 
reduced scale — e.g., if a drawing is to be made to the scale of 
2" = I ft., then 2" measured by the standard rule would be 
divided into 12 equal parts and each part would represent 1". 
See Fig. 8i£. 



1J 



MECHANICAL DRAWING. 



THE SCALE GUARD. 

This instrument is shown in No. 17 (in "The Complete 
Outfit "). It is employed to prevent the scale from turning, 
so that the draftsman can use it without having to look for 
the particular edge he needs every time he wants to Jay off 
a measurement. 

THE COMPASSES. 

When about to draw a circle or an arc of a circle, take 
hold of the compass at the joint with the thumb and two first 
fingers, guide the needle-point into the center and set the 
pencil or pen leg to the required radius, then move the thumb 
and forefinger up to the small handle provided at the top of 
the instrument, and beginning at the lowest point draw the 
line clockwise. The weight of the compass will be the only 
down pressure required. 






Fig. 16. 



The sharpening of the lead for the compasses is a very im- 
portant matter, and cannot be emphasized too much. Before 
commencing a drawing it pays well to take time to properly 
sharpen the pencil and the lead for compasses and to keep 
them always in good condition. 

The directions for sharpening the compass leads are the 
same as has already been given for the sharpening of the 
straight-line pencil. 



INSTRUMENTS. 



13 



THE DIVIDERS OR SPACERS. 

This instrument should be held in the same manner as de- 
scribed for the compass. It is very useful in laying off equal 
distances on straight lines or circles. To divide a given line 
into any number of equal parts with the dividers, say 12, it 
is best to divide the line into three or four parts first, say 4, 
and then when one of these parts has been subdivided accu- 
rately into three equal parts, it will be a simple matter to 
step off these latter divisions on the remaining three-fourths 




Fig. 17. 

of the given line. Care should be taken not to make holes in 
the paper with the spacers, as it is difficult to ink over them 
without blotting. 



THE SPRING BOWS. 

These instruments are valuable for drawing the small cir- 
cles and arcs of circles. It is very important that all the 



14 MECHANICAL DRAWING. 

small arcs, such as fillets, round corners, etc., should be care- 
fully pencilled in before beginning to ink a drawing. Many 
good drawings are spoiled because of the bad joints between 
small arcs and straight lines. 

When commencing to ink a drawing, all small arcs and 
small circles should be inked first, then the larger arcs and 
circles, and the straight lines last. This is best, because it is 
much easier to know where to stop the arc line, and to draw 
the straight line tangent to it, than vice versa. 

IRREGULAR CURVES. 

The irregular curve shown in Fig. 5 is useful for draw- 
ing irregular curves through points that have already been 
found by construction, such as ellipses, cycloids epicyloids, etc., 
as in the cases of gear-teeth, cam outlines, rotary pump wheels, 
etc. 

When using these curves, that curve should be selected 
that will coincide with the greatest number of points on the 
line required. 

THE PROTRACTOR. 

This instrument is for measuring and constructing angles. 
It is shown in Fig. 12. It is used as follows when measuring 
an angle: Place the lower straight edge on the straight line 
which forms one of the sides of the angle, with the nick 
exactly on the point of the angle to be measured. Then the 
number of degrees contained in the angle may be read from 
the left, clockwise. 

In constructing an angle, place the nick at the point from 
which it is desired to draw the angle, and on the outer circum- 



INSTR UMEN TS. 1 5 

ference of the protractor, find the figure corresponding to the 
number of degrees in the required angle, and mark a point on 
the paper as close as possible to the figure on the protractor; 
after removing the protractor, draw a line through this point 
to the nick, which will give the required angle. 



CHAPTER II. 
GEOMETRICAL DRAWING. 

The following problems are given to serve a double pur- 
pose : to teach the use of drawing instruments, and to point 
out those problems in practical geometry that are most useful 
in mechanical drawing, and to impress them upon the mind of 
the student so that he may readily apply them in practice. 

The drawing-paper for this work should be divided tem- 
porarily, with light pencil-lines, into as many squares and rec- 
tangles as may be directed by the instructor, and the drawings 
made as large as the size of the squares will permit. The 
average size of the squares should be not less than 4". When 
a sheet of drawings is finished these boundary lines may be 
erased. 

It will be noticed in the illustrations of this chapter that 
all construction lines are made very narrow, and given and 
required lines quite broad. This is sufficient to distinguish 
them, and employs less time than would be necessary if the 
construction lines were made broken, as is often the case. 

If time will permit, it is advisable to ink in some of these 

drawings toward the last. In that event, the given lines may 

be red, the construction lines blue, and the required lines 

black. 

But even when inked in in black, the broad and narrow 

16 



GEOMETRICAL DRAWING. I J 

lines would serve the purpose very well without the use of col- 
ored inks. 

The principal thing to be aimed at in making these draw- 
ings is accuracy of construction. All dimensions should be 
laid off carefully, correctly, and quickly. Straight lines join- 
ing arcs should be exactly tangent, so that the joints cannot 
be noticed. It is the little things like these that make or mar 
a drawing, and if attended to or neglected they will make or 
mar the draftsman. The constant endeavor of the student 
should be to make every drawing he begins more accurate, 
quicker and better in every way than the preceding one. 

A drawing should never be handed in as finished until the 
student is perfectly sure that he cannot improve it in any way 
whatever, for the act of handing in a drawing is the same, or 
should be the same, as saying This is the best that I can do; 
I cannot improve it ; it is a true measure of my ability to 
make this drawing. 

If these suggestions are faithfully followed throughout this 
course, success awaits any one who earnestly desires it. 

Fig. b i8. To BlSECT A Finite Straight Line. — With 
A and B in turn as centers, and a radius greater than the half 
of AB y draw arcs intersecting at E and F. Join EF bisect- 
ing AB at C. 

An arc of a circle may be bisected in the same way. 

pfg b ii; To Erect a Perpendicular at the End of 
THE Line. — Assume the points above the line as center and 
radius EB describe an arc CBD cutting the line AB in the 
point C. From C draw a line through E cutting the arc in 
D. Draw DB the perpendicular. 

Fi^'ao! The Same Problem: a Second Method. — 



i8 



MECHANICAL DRAWING. 



With center B and any radius as BC describe an arc CDE 
with the same radius; measure off the arcs CDa.nd DE. With 
D and E as centers and any convenient radius describe arcs in- 
tersecting at F. FB is the required perpendicular. 
'e 




Fig. 21. 

FiS^i*. To Draw a Perpendicular to a Line 
from a Point above or below It. — Assume the point 
C above the line. With center C and any suitable radius 
cut the line AB in E and F. From E and F describe'arcs 
cutting in D. Draw CD the perpendicular required. 



GE OME 7 RICA L DRA WIN G. 



19 



Fi2, b *22; To Bisect A Given Angle. — With A as center 
and any convenient radius describe the arc BC. With B and 
C as centers and any convenient radius draw arcs intersecting 
at D. Join AD, then angle BAD = angle DAC. 




Fig. 22. 

Fi^bf] To Draw a Line Parallel to a Given 
Line AB Through a Given Point C. — From any point 
on AB as B with radius BC describe an arc cutting AB in A, 
From C with the same radius describe arc BD. From B with 
AC as radius cut arc BD in D. Draw CD. Line CD is paral- 
lel to AB. 

J?. T\ 1 2) 




Fig. 23. 

Pi^aJ; From a Point D on the Line DE to set 
off an Angle equal to the given Angle BAC. — From 



20 



MECHANICAL DRAWING. 



* 



A with any convenient radius describe arc BC. From D wit 
the same radius describe arc EF. With center E and radius 
BC cut arc EF in F. Join DF. Angle EDF is = angle BAC. 




Fig. 24. 

FiS. b 25.' • To Divide an Angle into two equal 
Parts, when the Lines do not Extend to a Meeting 
Point. — Draw the line CD and CE parallel and at equal dis- 




Fig. 25. 



tances from the lines AB and FG. With C as center and any 
radius draw arcs 1,2. With 1 and 2 as centers and any con- 



GEOMETRICAL DRAWIXG. 21 

venient radius describe arcs intersecting at//". A line through 
C and H divides the angle into two equal parts. 

Fi2 b '2(3*. To Construct a Rhomboid having Adja- 
cent Sides equal to two Given Lines AB and AC, and 
an Angle equal to a Given Angle A. — Draw line DE 
equal to AD. Make D — angle A. Make DF — AC. From 
F with line AB as radius and from E with line AC as radius 
describe arcs cutting in G. Join FG and EG. 




Fi"g b ' 27*. To DlvIDE THE LlXE AB into any Number 
OF EQUAL Parts, SAY 15. — Draw a line CD parallel to AB, 
of any convenient length. From C set off along this line the 
number of equal parts into which the lineABis to be divided. 
Draw CA and DB and produce them until they intersect at 
E. Through each one of the points 1, 2, 3, 4, etc., draw 
lines to the point E, dividing the line AB into the required 
number of equal parts. 

This problem is useful in dividing a line when the point 
required is difficult to find accurately — e.g., in Fig. 28 AB is 
the pitch of the spur gear, partly shown, which includes a 



22 



MECHANICAL DRAWING. 



space and a tooth and is measured on the pitch circle. In 
cast gears the space is made larger than the thickness of the 
tooth, the proportion being about 6 to 5 — i.e., if we divide 
the pitch into eleven equal parts the space will measure T 6 T 




»cP^ 




q 1 & 3 4 S 6 7 89 1.011 1213 U J> 
Fig. 27. 




Fig 



and the tooth T 5 T . The T * T which the space is larger than the 
tooth is called the backlash. Let A'B' be the pitch chord of 
the arc AB. Draw CD parallel to A'B' at any convenient 
distance and set off on it 1 x . equal spaces of any convenient 
length. Draw CA' and DB' intersecting at E. From point 
5 draw a line to E which will divide A'B' as required; the 
one part yV and the other T 6 T . 

Fi2. b ' 2^ To DlvIDE A Given Line into any Number 
of Equal Parts: Another Method. — Let AB be the 
given line. From A draw A C at any angle, and lay off on it 
the required number of equal spaces of any convenient length. 
Join CB and through the divisions on AC draw lines parallel 
to CB, dividing AB as required in the points i', 2', 3', 4', etc. 

Mg. b " 30." To Divide a Line AB Proportionally to 
the Divided Line CD. — Draw AB parallel to CD at any 



. 



GEOMETRICAL DRAWING. 



23 



distance from it. Draw lines through CA and DB and produce 
them till they meet at E. Draw lines from E through the 
divisions I, 2, 3, 4, etc., of line CD, cutting line AB in the 




a l 



3 4 5 6 7 S 9 10 111213 U g 
Fig. 29. 



points 5, 6, 7, 8, etc. The divisions on AB will have the 
same proportion to the divisions on CD that the whole line 
AB has to the whole line CD — i.e., the lines will be propor- 
tionally divided. 




Fi^' 31I The Same : Another Method. — Let BC, 
the divided line, make any angle with BA, the line to be di- 



24 



MECHANICAL DRAWING. 



vided at B. Draw line CA joining the two ends of the lines. 
Draw lines from 5, 6, 7, 8, parallel to CA, dividing line AB 
in points 1, 2, 3, 4, proportional to BC 

Ffg. b * 32! To Construct an Equilateral Triangle 
on A Given Base AB, — From the points A and B with AB 
as radius describe arcs cutting in C. Draw lines AC and BC. 
The triangle ABC is equilateral and equiangular. 




Fig. 32. 



Mg b * 33. To Construct an Equilateral Triangle 
of a Given Altitude, AB. — From both ends of AB draw 
lines perpendicular to it as CA and DB. From A with any 
radius describe a semicircle on CA and with its radius cut off 
arcs 1, 2. Draw lines from A through 1, 2, and produce 
them until they cut the base BD. 

Ffg b *34. To Trisect a Right Angle ABC— From 
the angular point B with any convenient radius describe an 
arc cutting the sides of the angle in C and A. From C and A 
with the same radius cut off arcs 1 and 2. Draw lines \B and 
2B, and the right angle will be trisected. 



GEOMETRICAL DRAWING. 



25 



Fig. b * 35! To Construct any Triangle, its Three 
Sides AB and £7 being given. — From one end of the base 
as A describe an arc with the line B as radius. From the 
other end with line C as radius describe an arc, cutting the 
first arc in D. From D draw lines to the ends of line A, and a 
triangle will be constructed having its sides equal to the sides 
given. To construct any triangle the two shorter sides B and 
C must together be more than equal to the largest side A. 




Fig. 34. 



Fig. 35. 




Fig. 36. 




Fig. 37. 



Ffg b ' si! To Construct a Square, its Base AB 
Erect a perpendicular at B. Make BC equal 



Fig. 36 

BEING GIVEN 



26 



MECHANICAL DRAWING. 



to AB. From A and C with radius AB describe arcs cutting 
in D. Join DC and DA. 

Fi*g b * 37.' To Construct a Square, given its Di- 
agonal AB. — Bisect AB in C. Draw Z)/ 7 perpendicular to 
AB at C Make CD and £F each equal to CA. Join y2Z?, 
£>j5, BF, and FA. 

Fig. b * is! To Construct a Regular Polygon of any 
Number of Sides, the Circumscribing Circle being 
GIVEN. — At any point of contact, as C } draw a tangent AB 
to the given circle. From C with any radius describe a semi- 
circle cutting the given circle. Divide the semicircle into as 
many equal parts as the polygon is required to have sides, as 
I, 2, 3, 4, 5, 6. Draw lines from C through each division, 
cutting the circle in points which will give the angles of the 
polygon. 





Fi2 b ' io! Another Method. — Draw a diameter AB of 
the given circle. Divide AB into as many equal parts as 
the polygon is to have sides, say 5. From A and B with the 



GEOMETRICAL DRAWING. 



27 



line AB as radius describe arcs cutting in C, draw a line from 
C through the second division of the diameter and produce it 
cutting the circle in D. BD will be the side of the required 
polygon. The line C must always be drawn through the 
second division of the diameter, whatever the number of 
sides of the polygon. 

Fi£ b ' to.' To Construct any Regular Polygon 
with A GIVEN Side AB.— Make BD perpendicular and 
equal to AB. With B as center and radius AB describe arc 
DA. Divide arc DA into as many equal parts as there are 
sides in the required polygon, as 1, 2, 3, 4, 5. Draw B2. 
Bisect line AB and erect a perpendicular at the bisection cut- 
ting B2 in C. With C as center and radius CB describe a 
circle. With AB as a chord step off the remaining sides of 
the polygon. 





Fig. 40. 



Fig. 41. 



Fi r g b 'fi: Another Method.— Extend line AB. With 
center A and any convenient radius describe a semicircle. 
Divide the semicircle into as many equal parts as there are 
sides in the required polygon, say 6. Draw lines through 
every division except the first. With A as center and AB as 



28 MECHANICAL DRAWING. 

radius cut off A2 in C. From C with the same radius cut A3 
in D. From D, A\ in E. From B, A$ in F. Join AC, CD, 
DE, EF, and FB. 

Ffg b ' ft.' To Construct a Regular Heptagon, the 
Circumscribing Circle being given. — Draw a radius AB. 
With i? as center and BA as radius, cut the circumference in 
1,2; it will be bisected by the radius in C. Ci or C2 is equal 
to the side of the required heptagon. 




Fig. 42. 




Ffs. b * 43 To Construct a Regular Octagon, the 
Circumscribing Circle being given. — Draw a diameter 
AB. Bisect the arcs AB in C and D. Bisect arcs CA and 
CB in 1 and 2. Draw lines from 1 and 2 through the center 
of the circle, cutting the circumference in 3 and 4. Join A\, 
iC, C2, 2£ t i?3, etc. 

Ffg b * U To Construct a Pentagon, the Side AB 
BEING GIVEN. — Produce AB. With B as center and BA as 
radius, describe arc AD2. With center A and same radius, 
describe an arc cutting the first arc in D. Bisect AB in E. 



GEOMETRICAL DRAWING. 



2 9 



Draw line DE. Bisect arc BD in F. Draw line EF. With 
center C and radius EF cut off arc C\ and 1, 2 on the semi- 
circle. Draw line B2 ; it will be a second side of the penta- 




gon. Bisect it and draw a line perpendicular to it at the 
bisection. The perpendiculars from the sides AB and B2 
will cut in G. With G as center and radius GA describe a 
circle • it will contain the pentagon. 




Fig. 45. 



3° 



MECHANICAL DRAWING. 



^2 h ' 51' To Construct a Heptagon on a Given 

.rig. 4:0. 

LINE AB. — Extend line AB to C. From B with radius AB 
describe a semicircle. With center A and same radius de- 
scribe an arc cutting the semicircle in D. Bisect AB in E. 
Draw line DE. With C as center and DE as radius, cut off 
arc I on the semicircle. Draw line B\ ; it is a second side of 
the heptagon. Bisect it and obtain the center of the circum- 
scribing circle as in the preceding problem. 

Fig*. 15 ' Hi To Inscribe an Octagon in a Given 
Square. — Draw diagonals AD, CB intersecting at O. From 
A, B, C, and D with radius equal to AO describe quadrants 
cutting the sides of the square in I, 2, 3, 4, 5, 6, 7, 8. Join 
these points and the octagon will be inscribed. 




8 


/ 


< > 


\ 


i 




E 


F 








f \ 


/ 


^ 



Fig. 46. 



Fig. 47- 



Fig. b * I?.' To Construct a Regular Octagon on a 
Given Line AB. — Extend line AB in both directions. Erect 
perpendiculars at A and B. With centers A and B and radius 
AB describe the semicircle CEB and AF2. Bisect the quad- 
rants CE and DF in 1 and 2, then A\ and B2 will be two 
more sides of the octagon. At 1 and 2 erect perpendiculars 
1. 3 and 2, 4 equal to AB. Draw 1-2 and 3-4. Make the 



GEOMETRICAL DRAWING. 



3* 



perpendiculars at A and B equal to I -2 or 3-4 — viz., A$ and 
i>6. Complete the octagon by drawing 3-5, 5-6, and 6-4. 

Fi- b ' ±s. To Draw a Right Line Equal to Half 
THE ClRCUxMFERENCE OF A Given CIRCLE. — Draw a diam- 
eter AB. Draw line AC perpendicular to AB and equal to 
three times the radius of the circle. Draw another perpen- 
dicular at B to AB. With center B and radius of the circle 
cut off arc BD, bisect it and draw a line from the center of 
the circle through the bisection, cutting line B in E. Join 
EC. Line EC will be equal to half the circumference of 
circle A. 

. G 
A c 




Fig b " 49'. To Find A Mean Proportional to two 
Given Right Lines. — Extend the line AB to E making BE 
equal to CD. Bisect AE in F. From F with radius FA de- 
scribe a semicircle. At B where the two given lines are 
joined erect a perpendicular to AE cutting the semicircle in 
G. BG will be a mean proportional to CD and AB. 

Fi| b ' io. To FlND A Third Proportional (less) to 
two Given Right Lines AB and CD. — Make EF= the 
given line AB. Draw EG '= DC making an angle with EF. 
Join FG. From E with EG as radius cut EF in H. Draw 



3 2 



MECHANICAL DRAWING. 



H parallel to FG, cutting EG in /. EI is the third propor- 
tional (less) to the two given lines. 





A 



B 



D 



Fig. 50. 



F 

Fig. 51. 



Fi2. b * ii! To Find a Fourth Proportional to three 
Given Right Lines AB, CD, and EF.— Make ^^=the 
given line AB. Draw GI = CD, making any convenient 
angle to GH. Join HI. From G lay off GK = EF. From 
K draw a parallel to HI cutting GI in L. GL is the fourth 
proportional required. 





Fig. 53. 

Fi£ b §2! To Find the Center of a Given Arc ABC. 
— Draw the chords AB and CD and bisect them. Extend 
the bisection lines to intersect in D the center required. 



GEOMETRICAL DRAWING. 



33 



Fig b * 53.' To Draw a Line Tangent to an Arc of a 
CIRCLE. — (ist.) When the center is not accessible. Let B 
be the point through which the tangent is to be drawn. 
From B lay off equal distances as BE, BF. Join EF and 
through B draw ABC parallel to EF. (2d.) When the cen- 
ter D is given. Draw BD and through B draw ABC perpen- 
dicular to BD. ABC is tangent to the circle at the point B. 

mg h ' IS.' To Draw Tangents to the Circle C from 
THE POINTS WITHOUT It. — Draw^C and bisect it in E. 
From E with radius EC describe an arc cutting circle C in B 
and D. Join CB, CD. Draw AB and AD tangent to the 
circle C. 





Fig. 54. Fig. 55. 

Fi r g. b * 55! To Draw a Tangent between two Cir- 
cles. — -Join the centers A and B. Draw any radial line 
from A as A2 and make 1-2 = the radius of circle B. From 
A with radius A-2 describe a circle C2D. From center B 



34 



MECHANICAL DRAWING. 



draw tangents BC and BD to circle C2D at the points C and 
D by preceding problem. Join AC and ^4Z? and through 
the points E and F draw parallels FG and EH to BD and i?C. 
/^ and EH are the tangents required. 

Fi^' IS: To Draw Tangents to two Given Cir- 
cles A AND B.— Join ^ and B. From ^4 with, a radius 
equal to the difference of the radii of the given circles de- 





Fig. 56. 

scribe a circle GF. From B draw the tangents BF and BG y 
by Prob. 37. Draw AF and ^4£ extended to E and //. 
Through ii and H draw i:C and HD parallel to BF and BG 
respectively. EC and Z?77 are the tangents required. 

^' I?; To Draw an Arc of a Circle of Given 
Radius Tangent to two Straight Lines. — AB and AC 
are the two straight lines, and r the given radius. At a dis- 
tance = r draw parallels 1-2 and 3-4 to AC and ^4Z?, inter- 



GEOMETRICAL DRAWING. 



35 



secting at F. From F draw perpendiculars FD and FE. 
With F as center and FD or FE as radius describe the re- 
quired arc, which will be tangent to the two straight lines at 
the points D and E. 

Fi*£ b ' 5^; To Draw an Arc of a Circle Tangent 
to two Straight Lines BC and CD when the Mid- 
position G IS GIVEN. — Draw CA the bisection of the angle 
BCD and EF at right angles to it through the given point G. 
Next bisect either of the angles FEB or EFD. The bisection 
line will intersect the central line CA at A, which will be the 
center of the arc. From A draw perpendiculars Ai and A2, 
and with either as a radius and A as center describe an arc 
which will be tangent to the lines BC and CD at the points I 
and 2. 

f J>A 




Fig. 58. 



Fig?' 59'. To Inscribe a Circle within a Triangle 
ABC. — Bisect the angles A and B. The bisectors will meet 
in D. Draw Di perpendicular to AB. Then with center D 
and radius = D\ describe a circle which will be tangent to 
the given triangle at the points I, 2, 3. 

Ffg b * to'. To Draw an Arc of a Circle of Given 
Radius R tangent to two Given Circles A and B. — 
From A and B draw any radial lines as A$, B\. Outside 
the circumference of each circle cut off distances 1-3 and 2-4 



36 



MECHANICAL DRAWING. 



each =z the given radius R. Then with center A and radius 
A— 3, and center B and radius £-4 describe arcs intersecting at 
C. Draw CA,CB cutting the circles at 5 and 6. With centre 
C and radius C$ or C6 describe an arc which will be tangent 
at points 5 and 6. 




Prob. 43. 
Fig. 61. 



Fig. 60. 



To Draw an Arc of a Circle of Given 



Radius R tangent to two Given Circles A and B 




when the Arc includes the Circles. — Through A and B 
draw convenient diameters and extend them indefinitely. On 



GEOMETRICAL DRAWING. 



17 



these measure off the distances 1-2 and 3-4, each equal in 
length to the given radius R. Then with center A and radius 
A2 y center B and radius £4, describe arcs cutting at C. From 
C draw £~5 and C6 through B and A. With center C and ra- 
dius C6 or C$ describe the arc 6, 5, which will be tangent to 
the circles at the points 6 and 5. 

Fi?' 62! To Draw an Arc of a Circle of Given 
Radius R tangent to Two Given Circles A and B 
when the Arc includes one Circle and excludes the 
OTHER. — Through A draw any diameter and make 1-2 = R. 




Fig. 62. 



From B draw any radius and extend it, making 3-4 = R. With 
center A and radius A2 and center B and radius B4 describe 
arcs cutting at C. With C as center and radius = C$ or C6 
describe the arc 5, 6. 

Fi| b ' 63! Draw an Arc of a Circle of Given Ra- 
dius R tangent to a Straight Line AB and a Circle 
CD. — From £, the center of the given circle, draw an arc of a 



3° MECHANICAL DRAWING. 

circle i , 2 concentric with CD at a distance R from it, and 
also a straight line 3, 4 parallel to AB at the same distance R 
from ^4i?. Draw £(2 intersecting CD at 5. Draw the perpen- 
dicular 06. With center O and radius (96 or 0$ describe the 
required arc. 

2 




Fig. 63. 

FiJ b ' 64*. To Describe an Ellipse Approximately 
BY MEANS OF THREE RADII (F. R. Honey's method). — 




Fig. 64. 

Draw straight lines RH and //<2> making any convenient angle 
at H. With center /f and radii equal to the semi-minor and 



GEOMETRICAL DRAWING. 



39 



semi-major axes respectively, describe arcs LM and NO. Join 

LO and draw MK and NP parallel to LO. Lay off Zi = J 

of ZA r . Join <9i and draw M2 and ^3 parallel to Oi. Take 

//3 for the longest radius (= T), H2 for the shortest radius 

(= E), and one-half the sum of the semi-axes for the third 

radius (= S), and use these radii to describe the ellipse as 

follows: Let AB and CD be the major and minor axes. Lay 

off AAr = E and A^ = 5. Then lay off CG = T and C6 = 5. 

With £ as center and G6 as radius draw the arc 6, g. With 

center 4 and radius 4, 5, draw arc 5, g, intersecting 6, ^ at g. 

Draw the line Gg and produce it making £8 = T. Draw g, 

4 and extend it to 7 making g, 7 = S. With center G and 

radius GC(=T) draw the arc CS. With center £- and radius 

g y 8 ( = 5) draw the arc 8, 7. With center 4 and radius 4, 7 

(=E) draw arc 7^4. The remaining quadrants can be drawn 

in the same way. 

Fi2 b * 65 To Draw ax Ellipse having given the 

Axes AB AND CD. — Draw AB and CD at right angles to and 

bisecting each other at E. With center C and radius EA cut 

AB in F and F the foci. Divide EF or EF' into a number of 

parts as shown at 1, 2, 3, 4, etc. Then with F and F' as cen- 
c 




Fig. 65. 



Fig. 67. 



ters and ^4 1 and 2?i, and ^2 and ^2, etc., as radii describe arcs 
intersecting in i£, 5, etc., until a sufficient number of points 



4o 



MECHANICAL DRAWING. 



are found to draw the elliptic curve accurately throughout. 
(No. 5 of the "Sibley College Set" of irregular curves is 
very useful in drawing this curve.) To draw a tangent to 
the ellipse at the point G: Extend FG and draw the bisector 
of the angle HGF' ' . KG is the tangent required. 

pfg. b ' el; Another Method.— Let AB and AC be the 
semi axes. With A as center and radii AB and AC describe 
circles. Draw any radii as Al and A4., etc. Make 3 1, 42, 
etc., perpendicular to AB, and Z>2, E$, etc., parallel to AB. 
Then 1, 2, 5, etc., are points on the curve. 

Fig b * 6?'. Another Method. — Place the diameters as 
before, and construct the rectangle CDEF. Divide AB and 
DB and BF into the same number of equal parts as 1, 2, 3 and 
B. Draw from C through points 1, 2, 3 on AB and BD 
lines to meet others drawn from E through points 1, 2, 3 on 
AB and FB intersecting in points GHK. GHK are points on 
the curve. 

Fi*g b ' Is! Another Method.— Place the diameters AB 
and CD as shown in Drawing No. 1. Draw any convenient 
■1 ■ 

>L ,K 




H 






Fig. 68. 



angle RHQ, Drawing No. 2. With center //"and radii equal 
to the semi-minor and semi-major axes describe arcs LM and- 



GEOMETRICAL DRAWING. 4 1 

NO. Join LO and draw MK and NP parallel to LO. Then 
from C and Z> with a distance = ///* lay off the points I 1'on 
the minor axis and from A and B with a distance = HK lay 
off the points 2 2' on the major axis. With centers l,l', 2 and 
2' and radii i-Z> and 2 / -2?, respectively, draw arcs of circles. 
On a piece of transparent celluloid 7Tay off from the point G, 
GF and GE = the semi-minor and semi-major axes respec- 
tively. Place the point ^on the major axis and the point E on 
the minor axis. If the strip of celluloid is now moved over 
the figure, so that the point E is always in contact with the 
semi-minor axis and the point F with the semi major axis, the 
necessary number of points may be marked through a small 
hole in the celluloid at G with a sharp conical-pointed pencil, 
and thus complete the curve of the ellipse between the arcs of 
circles. 

FfS b ' I9! To Construct a Parabola, the Base CD 
and the Abscissa AB being given. — Draw EF through A 
parallel to CD and CE and DF parallel to AB. Divide AE, 
AF, EC, and FD into the same number of equal parts. 
Through the points 1, 2, 3 on AF and AE draw lines parallel 
to AB, and through A draw lines to the points 1,2, 3 on FD 
and EC intersecting the parallel lines in points 4, 5, 6, etc., of 
the curve. 

Fr2 b ' f §; Given the Directrix BD and the Focus C 
to Draw a Parabola and a Tangent to It at the Point 
3. — The parabola is a curve such that every point in the curve 
is equally distant from the directrix BD and the focus C. The 
vertix E is equally distant from the directrix and the focus, 
i.e. CE is = EB. Any line parallel to the axis is a diameter. 
A straight line drawn across the figure at right angles to the 



42 



MECHANICAL DRAWING. 



axis is a double ordinate, and either half of it is an ordinate. 
The distance from C to any point upon the curve, as 2 is 
always equal to the horizontal distance from that point to the 
directrix. Thus Ci = i, i' , C2 to 2, 2', etc. Through C 
draw ACF at right angles to BD, ACF is the axis of the 



Ai 2 3 F 








(6 


kI 


1 


cS 

x 


t£ 




D 


A 




6 





4 







\E 


B '> 




n 


1 




3 


2 




4 



Fig. 70. 

curve. Draw parallels to BD through any points in AB, and 
with center C and radii equal to the horizontal distances of 
these parallels from BD describe arcs cutting in the points I, 
2, 3, 4, etc. These are points in the curve. The tangent to 
the curve at the point 3 may be drawn as follows : Produce 
AB to F. Make EF = the horizontal distance of ordinate 33 
from E. Draw the tangent through $F. 

FiJ b * 71! To Draw an Hyperbola, having given 
the Diameter AB, the Abscissa BD, and Double Ordi- 
nate EF. — Make F4 parallel and equal to BD. Divide DF 
and F4 into the same number of equal parts. From B draw 
lines to the points in 4F and from A draw lines to the points 
in DF. Draw the curve through the points where the lines 
correspondingly numbered intersect each other. 



GEOMETRICAL DRAWING. 



43 



F?g b ' ?** To Construct an Oval the Width AB 



72. 



BEING GIVEN. — Bisect AB by the line CD in the point E, 
and with E as center and radius EA draw a circle cutting CD in 





Fig. 71. 



Fig. 72. 



F. From ^4 and i> draw lines through F. From A and B with 
radius equal to AB draw arcs cutting the last two lines in G 
and H. From F with radius /l7 describe the arc 67/ to meet 
the arcs AG and BH, which will complete the oval. 

fTS! 5 ' 73! GlVEN AN Ellipse to Find the Axes and 
Foci. — Draw two parallel chords AB and CD. Bisect each 
of these in E and F. Draw EF touching the ellipse in 1 and 
2. This line divides the ellipse obliquely into equal parts. 
Bisect I, 2 in G, which will be the center of the ellipse. From 
G with any radius draw a circle cutting the ellipse in HIJK. 
Join these four points and a rectangle will be formed in the 
ellipse. Lines LM and NO, bisecting the sides of the 
rectangle, will be the diameters or axes of the ellipse. With 
N or O as centers and radius = GL the semi-major axis, de- 
scribe arcs cutting the major axis in P and Q the foci. 

m^' 74'. To Construct a Spiral of one Revolu- 
tion. — Describe a circle using the widest limit of the spiral as 



44 



MECHANICAL DRAWING. 



a radius. Divide the circle into any number of equal parts as 
A, B, Cj etc. Divide the radius into the same number of equal 
parts as I to 12. From the center with radius 12, 1 describe 
an arc cutting the radial line B in i'. From the center con- 
tinue to draw arcs from points 2, 3, 4, etc., cutting the corre- 
sponding radii C, D, B, etc. in the points 2', 3', 4', etc. From 
12 trace the Archimedes Spiral of one revolution. 

B 





Fi^' 75. To Describe a Spiral of any Number of 
REVOLUTIONS, E.G., 2. — Divide the circle into any num- 
ber of equal parts as A, B, C, etc., and draw radii. Divide 
the radius A 12 into a number of equal parts corresponding 
with the required number of revolutions and divide these 
into the same number of equal parts as there are radii, viz., 
1 to 12. It will be evident that the figure consists of two 
separate spirals, one from the center of the circle to 12, and 
one from 12 to A. Commence as in the last problem, draw- 
ing arcs from I, 2, 3, etc., to the correspondingly numbered 
radii, thus obtaining the points marked 1', 2', 3', etc. The 
first revolution completed, proceed in the same manner to 
find the points 1", 2" , 3", etc. Through these points trace 
the spiral of two revolutions. 



GEOMETRICAL DRAWING. 



45 



Fi r 2 b ' I?.' To Construct the Involute of the Cir- 
cle 0. — Divide the circle into any number of equal parts 
and draw radii. Draw tangents at right angles to these radii. 
On the tangent to radius I lay off a distance equal to one 
of the parts into which the circle is divided, and on each of 





the tangents set off the number of parts corresponding to the 
number of the radii. Tangent 12 will then be the circumfer- 
ence of the circle unrolled, and the curve drawn through the 
extremities of the other tangents will be the involute. 

E[° b - 52* To Describe an Ionic Volute. — Divide the 

r iff. * * • 

given height into seven equal parts, and through the point 3 
the upper extremity of the third division draw 3, 3 perpen- 
dicular to AB. From any convenient point on 33 as a cen- 
ter, with radius equal to one-half of one of the divisions on 
AB, describe the eye of the volute NPNM, shown enlarged 
at Drawing No. 2. NN corresponds to line 3, 3, Drawing 
No. 1. Make PM perpendicular to NN and inscribe the 
square NPNM, bisect its sides and draw the square 11, 12, 



MECHANICAL DRA\ 



13, 14. Draw the diagonals 11, 13 and 12, 14 and divide 
them as shown in Drawing No. 2. At the intersections of 
the horizontal with the perpendicular full lines locate the 
points 1, 2, 3, 4, etc., which will be the centers of the quad- 
rants of the outer curve. The centers for the inner curve 
will be found at the intersections of the horizontal and per- 




/ 1 


2/ 


/JVc 


,2. 


P 


\l 2 \ 






' n — 


7/\ 








— 




l 

1 




x]/ 


r 


1 vH 


yff\ 


\hY 






1] 


\jj< 




,1 






y~5 


■ \\i 


> l z 1 






*T 






\ lc 


J \ 








U / 



M 
Fig. 77- 

pendicular broken lines, drawn through the divisions on the 
diagonals. Then with center 1 and radius iP draw arc FN, 
and with center 2 and radius 2N draw arc NM y with center 3 
and radius 3 M draw arc ML, etc. The inner curve is drawn 
in a similar way, by using the points on the diagonals indi- 
cated by the broken lines as centers. 

mg h ' ?»: To Describe the Cycloid.— AB is the di- 
rector, CB the generating circle, X a piece of thin transparent 
celluloid, with one side dull on which to draw the circle C. 
At any point on the circle C puncture a small hole with a 
sharp needle, and place the point C tangent to the director 
AB at the point from which the curve is to be drawn. Hold 
the celluloid at this point with a needle, and rotate it until 






GEOMETRICAL DRAWING. 



47 



the arc of the circle C intersects the director AB. Through 
the point of intersection stick another needle and rotate X 
until the circle is again tangent to AB, and through the punc- 
ture at C with a 4H pencil, sharpened to a fine conical point, 
mark the first point on the curve. So proceed until sufficient 
points have been found to complete the curve. 

(NOTE. — The thin celluloid was first used as a drawing 
instrument by Professor H. D. Williams, of Sibley College, 
Cornell University.) 

Ffg b ' 79. To Find the Length of a Given Arc of a 
CIRCLE APPROXIMATELY. — Let BC be the given arc. Draw 
its chord and produce it to A, making BA equal half the 



> 


x^ 


- 


f) 


c 




A 




B 



Fig. 78. 




Fig. 79. 



chord. With center A and radius AC describe arc CD cut- 
ting the tangent line BD at £>, and making it equal to the 
arc BC. 

Fig b * so! To Describe the Cycloid by the Old 
Method. — Divide the director and the generating circle into 
the same number of equal parts. Through the center a draw 
ag parallel to AB for the line of centers, and divide it as AB 
in the points £, c, d, e, f, and g. With centers/, e, d, etc., de- 
scribe arcs tangent to AB, and through the points of division 
on the generating circle 1,2, 3, etc., draw lines parallel to 



48 



MECHANICAL DRAWING. 



AB cutting the arcs in the points i', 2', 3', etc. These will be 
points in the curve. 

An approximate curve may be drawn by arcs of circles. 
Thus, taking/' as center and f'g' as radius, draw arc g'l'. 




Fig. 80. 



Produce \'f and 2' e' until they meet at the center of the 
second arc 2 f f, etc. 

To Describe the Epicycloid and the 



Prob. 63. 
Fig. 81. 



HYPOCYCLOID. — Divide the generating circle into any num- 
ber of equal parts, 1, 2, 3, etc., and set off these lengths from 
C on the directing circle CB as e' ', d\ c' , etc. From A the cen- 
ter of the directing circle draw lines through e\ d' , c , etc., cut- 
ting the circles of centers in e, d, c, etc. From each of these 
points as centers describe arcs tangent to the directing circle. 
From center A draw arcs through the points of division on 
the generating circle, cutting the arcs of the generating circles 
in their several positions at the points i', 2' , 3', etc. These 
will be points in the curve. 

&?*• ||; Another Method. — Draw the generating 
circle on the celluloid and roll it on the outside of the gener- 
ating circle BC for the Epicycloid, and on the inside for the 



GEOMETRICAL DRAWING. 



49 



Hypocycloid, marking the points in the curve 1,2, 3, etc., in 
similar manner to that described for the Cycloid. 



Fig. 82. 




Fig. 81. 



Fig. 83. 



F$. b '!!; To Draw THE ClSSOlD.— Draw any line AB 
and BC perpendicular to it. On BC describe a circle. From 
the extremity C of the diameter draw any number of lines, 
at any distance apart, passing through the circle and meeting 
the line AB in 1' , 2' , 3', etc. Take the length from A to 9 
and set it off from C on the same line to 9" '. Take the dis- 
tance from 8' to 8 and set it off from C on the same line to 
8", etc., for the other divisions, and through 9", 8", 7" , 6", 
etc., draw the curve. 



50 MECHANICAL DRAWING. 

FiS. b ' I2i To Draw Schiele's Anti-friction Curve. 
— Let AB be the radius of the shaft and Bi, 2, 3, 4, etc., its 
axis. Set off the radius AB on the straight edge of a piece 
of stiff paper or thin celluloid and placing the point B on the 
division 1 of the axis, draw through point A the line Ai. 
Then lower the straight edge until the point B coincides with 
2 and the points just touches the last line drawn, and draw 
#2, and so proceed to find the points a, b, c, etc. Through 
these points draw the curve. 








Fig. 85. 

Fig b ' %V. To Describe an Interior Epicycloid. — 
Let the large circle X be the generator and the small circle 
Y the director. Divide circle Y into any number of equal 
parts, as B, H, /, /, etc. Draw radial lines and make HC, 
ID, JE, KF y etc., each equal to the radius of the generator 
X. With centers C, D, E, etc., describe arcs tangent at 
H, I, J, etc. Make Hi equal to one of the divisions of the di- 
rector as BH. Make I2 equal to two divisions, /3, three divi- 
sions, etc., and draw the curve through the points 1, 2, 3, 4, 



GEOMETRICAL DRAWING. 



51 



etc. This curve may also be described with a piece of cellu- 
loid in a similar way to that explained for the cycloid. 

It may not be out. of place here to describe a few of the 



MOULDINGS USED IN ARCHITECTURAL WORK, 

since they are often found applied to mechanical constructions. 
Fi2 b ' so! To Describe the "Scotia." — 1, 1 is the top 
line and 4, 4 the bottom line. From 1 drop a perpendicular 
I, 4; divide this into three equal parts, as 1, 2, and 3. 
Through the point 2 draw ab parallel to I, 1. With center 2 
and radius 2, 1 describe the semicircle alb, and with center b 
and radius ba describe the arc #5 tangent to 4, 4 at 5, draw 
the fillets 1, 1 and 4, 4. 



1 


1 


A 


?\ 


Q 


^ * 


& Jh- 




Fig. 86. 



Fig. 87. 



prob. 69. To Describe the "Cyma Recta."— Join 1, 
3 and divide it into five equal parts, bisect 1, 2 and 2, 3, and 
with radius equal to 1, 2 and 2, 3 respectively describe arcs 
1, 2 and 2,3. Draw the fillets 1, 1 and 3, 3 and complete the 
moulding. 

Fig*' 88.' To Describe the "Cavetto" or "Hol- 
low." — Divide the perpendicular 1, 2 into three equal parts 
and make 2, 3 equal to two of these. From centers 1 and 3 
with a radius somewhat greater than the half of 1, 3, describe 
arcs intersecting at the center of the arc 1, 3, 



52 



MECHANICAL DRAWING. 



Ffg b ' sh'. To Describe the " Echinus," ''Quarter 
Round," or "Ovolo." — Draw I, 2 perpendicular to 2, 3, 
and divide it into three equal parts. Make 2, 3 equal to 
two of these parts. From the points 2 and 3 with a radius 
greater than half 1,3, describe arcs cutting in the center of 
the required curve. 

1 ' li. M 




Fig 89. 



Fi° b * 90 To Describe the " Apophygee. 



Divide 

3^ 4 into four equal parts and lay off five of these parts from 
3 to 2. From points 2 and 4 as centers and radius equal to 
2,3, describe arcs intersecting in the center of the curve. 





Fig. 90. 

Fig b ' 91! To Describe the "Cyma Reversa." — Make 
4, 3 = 4, I. Join I, 3 and bisect it in the point 2. From the 
points 1, 2 and 3 as centers and radii equal to about two-thirds 
of 1 , 2 draw arcs intersecting at 5 and 6. Points 5 and 6 
are the centers of the reverse curves. 

Fi£ b ' It'. To Describe the " Torus."— Let 1, 2 be the 
breadth. Drop the perpendicular 1, 2, and bisect it in the 



GEOME TRICAL DRA WING. 



53 



point 3. With 3 as center and radius 3, I, describe the semi- 
circle. Draw the fillets. 






Fig. 92. 



Fig. 93. 



F%. b ' 9§i An Arched Window Opening. — The curves 
are all arcs of circles, drawn from the three points of the equi- 
lateral triangle, as shown in the figure. 

Fi r s b *94: To Describe the " Trefoil."— The equi- 
lateral triangle is drawn first, and the angle 1,2,3 bisected by 
the line 2, 4, which also cuts the perpendicnlar line 1, 6 in the 
point 6. The center of the surrounding circles 1, 2 and 3 are 
the centers of the trefoil curves. 

Fi r - b, 95. To Des cribe the " Quatre Foil."— Draw 
the square 1,2, 3, 4 in the position shown in the figure. The 
center of the surrounding circles, point 5, is at the intersection 
of the diagonals of the square. Points I, 2, 3, 4 of the square 
are the centers of the small arcs. 

Fig. b ' 9e! To Describe the "Cinquefoil Orna- 
ment." The curves of the cinquefoil are described from the 
corners of a pentagon 1, 2, 3, 4, 5. Bisect 4, 5 in 6 and draw 
2, 6, cutting the perpendicular in the point 7, the center of 
the large circles. 

Fi*g b ' 97.' To Draw a Baluster. — Begin by drawing 
the center line, and lay off the extreme perpendicular height, 



54 



MECHANICAL DRAWING. 



the intermediate, perpendicular, and horizontal dimensions, 
and finally the curves as shown in the figure. 



Fig. 94. 



Fig. 95. 



Fig. 96. 




Fig. 97. 



DRAWING TO SCALE. 

When we speak of a drawing as having been made to scale, 
we mean that every part of it has been drawn proportionately 
and accurately, either full size, reduced ox enlarged. 

Very small and complicated details of machinery are usu- 
ally drawn enlarged ; larger details and small machines may 
be made full size, while larger machines and large details are 
shown reduced. 

When a drawing of a machine is made to a reduced or en- 
larged scale the figures placed upon it should always give the 
full-size dimensions, i.e., the sizes the machine should meas 
ure when finished. 



GEOMETRICAL DRAWING. 



55 



Fig b ' 98.' To Construct a Scale of Third Size or 
4."= 1 FOOT. — Draw upon a piece of tough white drawing- 
paper two parallel lines about \" apart and. about 14" long as 
shown by a, Fig. 98. From A lay off distances equal to 4" 
and divide the first space AB into 12 equal parts or inches by 
Prob. 12. Divide AE'm the same way into as many parts as 

it may be desired to subdivide the inch divisions on AB, 
E 




21 



11W\8'7 (4\ 2 1 



gcule I'* lfoot. 



$' 5f 



Fig. 98. 

usually 8. When the divisions and subdivisions have been 
carefully and lightly drawn in pencil, as shown by a, in Fig. 
98, then the lines denoting jr"* i"> i", 1" ', and 3" should be 
carefully inked and numbered as shown by (b). By a further 
subdivision a scale of 2"= 1 foot may easily be made as shown 
by (c) in Fig. 98. 



CHAPTER III. 
CONVENTIONS. 

It is often unnecessary if not undesirable to represent cer- 
tain things as they would actually appear in a drawing, espe- 
cially when much time and labor is required to make them 
orthographically true. 

So for economic reasons draftsmen have agreed upon con- 
ventional methods to represent many things that would other- 
wise entail much extra labor and expense, and serve no par- 
ticular purpose. 

It is very necessary, however, that all draftsmen should 
know how to draw these things correctly, for occasions will 
often arise when such knowledge will be demanded ; and be- 
sides it gives one a feeling of greater satisfaction when using 
conventional methods to know that he could make them artis- 
tically true if it was deemed necessary. 

STANDARD CONVENTIONAL SECTION LINES. 

Conventional section lines are placed on drawings to distin- 
guish the different kinds of materials used when such drawings 
are to be finished in pencil, or traced for blue printing, or to 
be used for a reproduction of any kind. 

Water-colors are nearly always used for finished drawings 

and sometimes for tracings and pencil drawings. 

The color tints can be applied in much less time than it 

56 



CONVENTIONS. 57 

takes to hatch-line a drawing. So that the color method 
should be used whenever possible. 

FlG. 99. — This figure shows a collection of hatch-lined 
sections that is now the almost universal practice among 
draftsmen in this and other countries, and may be considered 
standard. 

No. 1. To the right is shown a section of a wall made of 
rocks. When used without color, as in tracing for printing, 
the rocks are simply shaded with India ink and a 175 Gillott 
steel pen. For a colored drawing the ground work is made 
of gamboge or burnt umber. To the left is the conventional 
representation of water for tracings. For colored drawings 
a blended wash of Prussian blue is added. 

No. 2. Convention for Marble. — When colored, the 
whole section is made thoroughly wet and each stone is then 
streaked with Payne's gray. 

No. 3. Convention for Chestnut. — When colored, a 
ground wash of gamboge with a little crimson lake and burnt 
umber is used. The colors for graining should be mixed in a 
separate dish, burnt umber with a little Payne's gray and 
crimson lake added in equal quantities and made dark enough 
to form a sufficient contrast to the ground color. 

No. 4. General Convention for Wood. — When colored the 
ground work should be made with a light wash of burnt sienna. 
The graining should be done with a writing-pen and a dark 
/nixture of burnt sienna and a modicum of India ink. 

No. 5. Convention for Black Walnut. — A mixture of 
Payne's gray, burnt umber and crimson lake in equal quanti- 
ties is used for the ground color. The same mixture is used 
for graining when made dark by adding more burnt umber. 



58 



MECHANICAL DRAWING. 




CON VEN TIOXS. 5 9 

No. 6. Convention for Hard Pine. — For the ground 
color make a light wash of crimson lake, burnt umber, and 
gamboge, equal parts. For graining use a darker mixture of 
of crimson lake and burnt umber. 

No. 7. Convention for Building-stone. — The ground 
color is a light wash of Payne's gray and the shade lines are 
added mechanically with the drawing-pen or free-hand with 
the writing-pen. 

No. 8. Convention for Earth. — Ground color, India ink 
and neutral tint. The irregular lines to be added with a writ- 
ing-pen and India ink. 

No. 9. Section Lining for Wrought or Malleable Iron. — 
When the drawing is to be tinted, the color used is Prussian 
blue. 

No. 10. Cast Iron. — These section lines should be drawn 
equidistant, not very far apart and narrower than the body 
lines of the drawing. The tint is Payne's gray. 

No. 1 1. Steel. — This section is used for all kinds of steel. 
The lines should be of the same width as those used for cast- 
iron and the spaces between the double and single lines should 
be uniform. The color tint is Prussian blue with enough crim- 
son lake added to make a warm purple. 

No. 12. Brass. — This section is generally used for all 
kinds of composition brass, such as gun-metal, yellow metal, 
bronze metal, Muntz metal, etc. The width of the full lines., 
dash lines and spaces should all be uniform. The color tint 
is a light wash of gamboge. 

Nos. 13-20. — The section lines and color tints for these 
numbers are so plainly given in the figure that further instruc- 
tion would seem to be superfluous. 



6o 



MECHANICAL DRAWING. 



VISIBLE OBJECT LINES 
Weight varied with discretion to suit 
size of part. 

INVISIBLE OBJECT LINES 
Length of dash not less than \" nor 
mo/i than tr", when possible space be- 
tween dashes very short, not more than 
3V'. dashes should be uniform in length 
ani spaces uniform in width. 

DIMENSION LINES 
Continuous lines broken only to admit 
the dimensions. 

CENTER LINES 
Long dashes, dots not more than 3V 
long, space between dash and dot quite 
short. 

DIMENSION, PROJECTION LINES' 
WITNESS LINES OR EXTEN- 
SION LINES 
First dash touching object tV" long, 

short space, then dashes about \" long. 

BREAK LINES 
These lines to be drawn freehand with 
the lettering pen. 

ADJACENT PART LINES 
Dashes \" long, dots not more than -h" 
long, and space quite short. 

ALTERNATE POSITION LINES 
Use A when the limiting position is in- 
dicated by a center line only, dashes f" 
and dots \" long, very close together. 
Use B when the alternate position is 
shown by the base outlines of the object. 
Dash £•", dot £", very close together. 

CUTTING PLANE LINES 
A dashes about f" long and all the 
same length, dots ■&" long, close together. 
Use B when it is not convenient to draw 
the line through the view. 



Heavy 
h" 



BORDER LINES; REFERENCE 
ARROW LINES 



Should always be drawn straight with 
ruling pen and set obliquely, i.e., neither 
vertically nor horizontally. 

Fig. 100. 
CONVENTIONAL LINES. 
Fig. 100. — There are four kinds: 

(1) The Hidden Line. — This line should be made of short 
dashes of uniform length and width, both depending some- 
whta on the size of the drawing. The width should always 



CONVENTIONS. 6l 

be slightly less than the body lines of the drawing, and the 
length of the dash should never exceed £'\ The spaces 
between the dashes should all be uniform, quite small, never 
exceeding T \". This line is always inked in with black ink. 

(2) The Line of Motion. — This line is used to indicate 
point paths. The dashes should be made shorter than those of 
the hidden line, just a trifle longer than dots. The spaces 
should of course be short and uniform. 

(3) Center Lines. — Most drawings of machines and parts 
of machines are symmetrical about their center lines. When 
penciling a drawing these lines may be drawn continuous and 
as fine as possible, but on drawings for reproductions the black- 
inked line should be a long narrow dash and two short ones 
alternately. When colored inks are used the center line should 
be made a continuous red line and as fine as it is possible to 
make it. 

(4) Dimension Lines and Line of Section. — These lines 
are made in black with a fine long dash and one short dash 
alternately. In color they should be continuous blue lines. 
Colored lines should be used wherever feasible, because they 
are so quickly drawn and when made fine they give the drawing 
a much neater appearance than when the conventional black 
lines are used. Colored lines should never be broken. 

CONVENTIONAL BREAKS. 

FlG. 10 1. — Breaks are used in drawings sometimes to indi- 
cate that the thing is actually longer than it is drawn, some- 
times to show the shape of the cross-section and the kind of 
material. Those given in Fig. 10 1 show the usual practice. 



62 



MECHANICAL DRAWING. 



CROSS-SECTIONS. 
FIG. 102. — When a cross-section of a pulley, gear-wheel 
or other similar object is required and the cutting-plane passes 



IT 



MMAWAmm^ «a mi mmmmvmvw; 



■M.WM.VWAVVVVVVVV\VV^VVvkV^W'0 



Fig. ioi. 




Fig. 102. 
through one of the spokes or arms, then only the rim and hub 
should be sectioned, as shown at xx No. I and z No. 2, and 
the arm or spoke simply outlined. Cross-sections of the arms 
may be made as shown at AA No. 2. In working drawings of 
gear-wheels only the number of teeth included in one quadrant 
need be drawn; the balance is usually shown by conventional 
lines, e.g., the pitch line the same as a center line, viz., a long dash 
and two very short ones alternately or a fine continuous red line. 
The addendum line (d) and the root or bottom line (b) the 
same as a dimension line, viz., one long dash and one short 



CONVENTIONS. 



63 



dash alternately or a fine continuous blue line. The end ele- 
vation of the gear-teeth should be made by projecting only 
the points of the teeth, as shown at No. 2. 



CONVENTIONAL METHODS OF SHOWING SCREW-THREADS 
IN WORKING DRAWINGS. 

FlG. 103. — No. I, shows the convention for a double 
V thread, U. S. standard; No. 2, a single V thread; No. 3, 
a single square thread; No. 4, a single left-hand V thread; 
No. 5, a double right hand square thread; No. 6, any 
thread of small diameter; No. 7, any thread of very small 
diameter. The true methods for constructing these threads 
are explained on pages 99-101, Figs. 137— 139. 

In No. 6. the short wide line is equal to the diameter 
of the thread at the bottom. The distance between the 
longer narrow lines is equal to the pitch, and the inclination 
is equal to half the pitch. 

The short dash lines in No. 7 should be made to corre- 




it ntj 




Fig. 103. 

spond to the diameter of the thread at the bottom. After 
some practice these lines can be drawn accurately enough by 
the eye. 



CHAPTER IV. 
LETTERING AND FIGURING. 

THIS subject has not been given the importance it deserves 
in connection with mechanical drawing. Many otherwise ex- 
cellent drawings and designs as far as their general appearance 
is concerned have been spoiled by poor lettering and figuring. 

All lettering on mechanical drawings should be plain and 
legible, but the letters in a title or the figures on a drawing 
should never be so large as to make them appear more prom- 
inent than the drawing itself. 

The best form of letter for practical use is that which gives 
the neatest appearance with a maximum of legibility and re- 
quires the least amount of time and labor in its construction. 

This would naturally suggest a " free-hand " letter, but be- 
fore a letter can be constructed " free-hand " with any degree 
of efficiency, it will be necessary to spend considerable time 
in acquiring a knowledge of the form and proportions of the 
particular letter selected. 

It is very desirable then that after the stud.ent has care- 
fully constructed as many of the following plates of letters and 
numbers as time will permit and has acquired a sufficient 
knowledge of the form and proportions of at least the " Ro- 
man " and " Gothic " letters; he should then adopt some one 

6 4 



LETTERING AND FIGURING. 65 

style and practice that at every opportunity, until he has at- 
tained some proficiency in its free-hand construction. 

When practicing the making of letters and numbers free- 
hand, they should be made quite large at first so as to train 
the hand. 

The " Roman " is the most legible letter and has the best 
appearance, but is also the most difficult to make well, either 
free-hand or mechanically. However, the methods given for 
its mechanical construction, Figs. 104 and 105, will materially 
modify the objections to its adoption for lettering mechanical 
drawings. 

The " Gothic" letter is a favorite with mechanical drafts- 
men, because it is plain and neat and comparatively easy to 
construct. (See Fig. 106.) 

Among the type specimens given in the following pages 
the Bold-face Roman Italic on page 70 is one of the best 
for a good, plain, clear, free-hand letter, and is often used 
with good success on working drawings. Gillott's No. 303 
steel pen is the best to use when making this letter free-hand. 

The "Yonkers" is a style of letter that is sometimes 
used for mechanical drawings. It is easy to construct with 
either F. Soennecken's Round Writing-pens, single point, or 
the Automatic Shading-pen. But it lacks legibility, and is 
therefore not a universal favorite. 

A good style for " Notes" on a drawing is the ''Gothic 
Condensed " shown on page 70. 

W r hen making notes on a drawing with this letter, the 
only guides necessary are two parallel lines, drawn lightly in 
pencil. The letters should be sketched lightly in pencil first, 



66 



MECHANICAL DRAWIXG. 



and then carefully inked, improving spacing and proportions 
to satisfy the practiced eye. 



FIGURING. 

Great care should be taken in figuring or dimensioning a 
mechanical drawing, and especially a working drawing. 

To have a drawing accurately, legibly, and neatly figured 
is considered by practical men to be the most important part 
of a working drawing. 

There should be absolutely no doubt whatever about the 
character of a number representing a dimension on a drawing. 

Many mistakes have been made, incurring loss in time, 
labor, and money through a wrong reading of a dimension. 

Drawings should be so fully dimensioned that there will 
be no need for the pattern-maker or machinist to measure any 
part of them. Indeed, means are taken to prevent him from 
doing so, because of the liability of the workman to make 
mistakes, so drawings are often made to scales which are dif- 
ficult to measure with a common rule, such as 2" and 4" = 
1 ft. 

The following books, among the best of their kind, are 
recommended to all who desire to pursue further the study 
of " Lettering" : Plain Lettering, by Prof. Henry S. Jacoby, 
Cornell University, Ithaca, N. Y. ; Lettering, by Charles W. 
Reinhardt, Chief Draftsman, Engineering News, New York ; 
Free-hand Lettering, by F. T. Daniels, instructor in C. E. in 
Tufts College. 



LETTERING AND FIGURING. 



6 7 





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68 



MECHANICAL DRAWING. 





m 




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si 




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52 



n 



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LETTERING AND FIGURING. 



69 




70 MECHANICAL DRAWING. 

18-Point Roman. 



ABCDEFGHIJKLMNOPQKSTUVWX 
YZ abcdefghijklmnopqrstuvwxyz 
1234567890 



[8-Point Italic. 



ABCDEFGHIJKLMNOPQRSTUV 

WX YZ abcdefghijklmnopqrs tuvwxyz 

i?.- Point Cushing Italic. 

ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklm 
nopqrstuvwxyz 123456 7890 

28-Point Boldface Italic. 

ABCDEFGHIJKLM 
NOPQRSTUVWXYZ 

abcdefghijklmnopqrstu 
vwxyz 12S4S67890 

Two-Line Nonpareil Gothic Condensed. 

ABCDEFGHIJKLMNOPQRSTUVWXYZ 1234567890 

Three-Line Nonpareil Lightface Celtic. 

ABCDEFGHIJKLMNOPQR 

STUVWXYZ abedefghijkl 
mnopqrstu vwxyz 
1234567890 " 



LETTERING AND FIGURING. *]\ 

18-Point Chelsea Circular. 

ABCDEFGHIJKLMNOPQRSTUVWX 

YZ abcdefgh(ijl\lmT^opqrstuvwxyz 

1234567890 

x8-Point Elandkay. 

ABCDEFGHIJKLnNOFQRSTUVVXYZ 
1234567890 

18-Point Quaint Open. 

WITZ 1 234 J67SS© 

28-Point Roman. 

ABCDEFGHIJKLM 
NOPQRSTUVWXYZ 

abcdefghij klmnopqrstu 
vwxyz 1234567890 



28-Point Old-Style Italic. 



ABCDEFGHIJKLMNOP 

QRSTUVM/XYZ abcdefg 
h ijklm n opqrstuvwxyz 
12345678QO 



72 MECHANICAL DRAWING. 

12-Point Victoria Italic. 

ABCDEFCHIJKLMNOPQRSTU 
YWXYZ 1234567890 

18-Point DeVinne Italic. 

ABCDEFGHIJKLMNOPQRSTV 

VWXYZ abcdefghijklmnopqrst 

uvwxyz 1234567890 

22-Point Gothic Italic. 

ABCDEFGHIJKLMNOPQRSTUVWXYZ 

abcdefghijklmnopqrstuuwxyz 

1234567890 

Double- Pica Program. 



ABCDEFGHIJKLMNO 



PQRSTUYWXYZ 

abcdefghijklmnopqrstuv 

wxyz 1234567890 



Nonpareil Telescopic Gothic. 

ABCDEFGHIJKLMNOPQRSTUVWXYZ 1234567S90 



LETTERING AND FIGURING. 73 

24-Point Gallican. 



ABCDEFGHIJKL 
MNOPQRSTUVW 
XYZ 1234567890 

Two-Line Virile Open. 

JBCPETQHUHi\M0PQR5TH»WXYZ 

4WefgWJHiw©p^jrst(ia^¥xp 
3456F8 



, AG] 

(0) 



22-Point Old-Style Roman. 

ABCDEFGHIJKLMNOPQRST 

UVWXYZ abcdefghijklmnopqrst 

uvwxyz 1234567890 



36-Point Yonkers. 




i 

y^ ctbcMgfyijklmnopqr 
stutwxya 1(23^567890 



CHAPTER V. 
ORTHOGRAPHIC PROJECTION. 

Orthographic Projection, sometimes called Descrip- 
tive Geometry and sometimes simply Projection, is one of 
the divisions of descriptive geometry; the other divisions are 
Spherical Projection, Isometric Projection, Shades and 
Shadows, and Linear Perspective. 

In this course we will take up only a sufficient number of 
the essential principles of Orthographic Projection, Isometric 
Projection, and Shades and Shade Lines, to enable the stu- 
dent to make a correct mechanical drawing of a machine or 
other object. 

Orthographic Projection is the science and the art of rep- 
resenting objects on different planes at right angles to each 
other, by projecting lines from the point of sight through the 
principal points of the object perpendicular to the Planes of 
Projection, 

There are commonly three planes of projection used, viz., 
the H. P. or Horizontal Plane y the V. P. or Vertical Plane, 
and the Pf P. or Profile Plane. 

These planes, as will be seen by Figs. 107 and 109, inter- 
sect each other in a line called the /. L. or Intersecting Line, 
and form four angles, known as the first, second, third, and 

74 



OR THO GRA PHIC PR OJE C TION, 



75 



fourth Dihedral Angles. Figs. 107 and 109 are perspective 
views of these angles. 

An object may be situated in any one of the dihedral 
angles, and its projections drawn on the corresponding co- 
ordinate planes. 

Problems in Descriptive Geometry are usually worked out 
in the first angle, and nearly all English draftsmen project 
their drawings in that angle, but in the United States the 
third angle is used almost exclusively. There is good reason 
for doing so, as will be shown hereafter. 

We will consider first a few projection problems in the 

first angle, after which the third angle will be used throughout. 

v 




Fig. 107. 

H.P., Fig. 107, is the Horizontal Plane, V.P. the Vertical 
Plane, and I.L. the Intersecting Line. 

The Horizontal Projection of a point is where a perpen- 
dicular line drawn through the point pierces the H.P. 

The Vertical Projection of a point is where a per. line 
drawn through the point pierces the V.P. 

Conceive the point a, Fig. 107, to be situated in space 4" 
above the H.P. and 3" in front of the V.P. If a line is 
passed through the point a per. to H.P. and produced until 



76 MECHANICAL DRAWING. 

it pierces the H.P. in the point a h , a h will be the Hor. Proj. 
of the point a. 

If another line is projected through the points per. to the 
V.P. until it pierces the V.P. in the point a v , a v is the ver- 
tical projection of the point a. 

If now the V.P. is revolved upon its axis I.L. in the di- 
rection of the arrow until it coincides with the H.P. and let 
the H.P. be conceived to coincide with the plane of the 
drawing-paper, the projections of the point a will appear as 
shown by Fig. 108. 

The vertical projection a v 4" above the I.L. and the 
horizontal projection a h 3" below the I.L. both in the same 
straight line. 

In mechanical drawing the vertical projection cC is called 
the Elevation and the horizontal projection a h the Plan. 

The projections of a line are found in a similar manner, 
by first finding the projections of the two ends of the line, 
and joining them with a straight line. 

Let ab be a line in space i\" long, parallel to the V.P. 
and perpendicular to the H.P. One end is resting on the 
H.P. 2i" from the V.P. 

The points a and b will be vertically projected in the 
points a v and b v . Join a v b v . a v b v is the vertical projection of 
the line ab. 

When a line is perpendicular to one of the planes of pro- 
jection, its projection on that plane is a point, and the projec- 
tion on the other plane is a line equal to the line itself. 

ab, Fig. 107, is perpendicular to the H.P., therefore its 
proj. on the H.P. when viewed in the direction ab will be 
seen to be a point. 



ORTHOGRAPHIC PROJECTION. 



77 



Conceive now the V.P. revolved as before, the V. proj. 
will be found to be at a v b v , Fig. 108, and the H. proj. at the 
point a h . 

cd, Fig. 107, is a line parallel to the H.P. and perpendic- 
ular to the V.P. Its elevation or V. proj. is the point d v , Fig. 
108, and its plan or H. proj. the line (^d h perpendicular to 
the Intersecting Line and equal in size to the line itself. 

Planes or Plane Surfaces bounded by lines are projected 
by the same principles used to project lines and points. 

Let aa v b v b, Fig. 107, be a plane at right angles to and 
touching both planes of projection. 

The elevation of the front upper corner a is projected in 
the point a v . The elevation of the front lower corner b is pro- 
jected in the point b° , Join a v b v . a v b v is the vertical projection 
of the front edge ab of the plane. The plan of the front 





a 

* 
b 


d 


V 


C 












ft 


c 

d 















Fig. 108. 

upper corner is projected in the point b and the point a v in the 
point b v . A straight line joining bb v is the plan or horizontal 
projection of the top edge of the plane. 

On the drawing-paper the plan and elevation of the plane 
acfb a would be shown as a continuous straight line a to a h 
Fig. 108. 



78 



MECHANICAL DRAWING 



Solids bounded by plane surfaces are projected by means 
of the same principles used to project planes, lines, and points. 

C, Fig. 107, is a cube bounded by six equal sides or sur- 
faces. The top and bottom being parallel to the H.P. and 
the front and back parallel to the V.P., the vert. proj. is a 
square above I.L. equal in area to any one of the six faces 
of the cube. The hor. proj. is a similar square belowT.L. 

These projections are shown at C, Fig. 108, as they would 
appear on the drawing-paper. 

The foregoing illustrates a few of the simple principles of 
projection in relation to points, lines, and solids when placed 
in the first dihedral angle, and we find that the plan is always 
below and the elevation always above the I.L. 

Let us now consider the same problems when situated in 
the third angle. The point a, Fig. 109, is behind the V.P. 




Fig. 109. 



and below the H.P. Draw through a perpendiculars to the 
plane of projection. The Hor. proj. is found at a h and the 
vert. proj. at a v . 

Conceive again the V.P. to be revolved in the direction 
of the arrow until it coincides with the H. P. The hor. proj. 



ORTHOGRAPHIC PROJECTION. 



79 



will then appear at a h above the I.L. and the vert. proj. at a v 
below the I.L., Fig. no. And so with the lines, the planes, 
and the solids. 



K 


d K 


K 

a 




a 

1 1 






C 






\ 










r. 


c 










-b ' 












x 


U" 


v 




a 




a> 





Fig. iio. 



In order to still further explain the use of the planes of 
projection, with regard to objects placed in the third angle, 
let us suppose a truncated pyramid surrounded by imaginary 
planes at right angles to each other, as shown by Fig. ill. 




Fig. hi. 

With a little attention it will easily be discerned that the 
pyramid is situated in the third dihedral angle, and that in 
addition to the V. and H. planes, we have passed two profile 
planes at right angles to the V. and H. planes, one at the right- 
hand and one at the left. 

When the pyramid is viewed orthographically through 
each of the surrounding planes, four separate views are had, 



8o 



MECHANICAL DRAWING. 



exactly as shown by the projections on the opposite planes, 
viz., a Front View, Elevation, or Vert. Proj. at F. ; a Right- 
hand View, Right-end Elevation, or Right-profile Projection 
at R. ; a Left-hand View, Left-end Elevation, or Left-profile 
Projection at L. ; a Top View, Plan or H. Proj. at P. 

If we now consider the V.P. and the right and left profile 
planes to be revolved toward the beholder until they coincide, 
using the front intersecting lines as axes, the projections of the 
pyramid will be seen as shown by Fig. 1 12, which when the 







p 










\ 












1 












/ 




\ 














f: 












^ 




































\ 




/ 


\ 






A 






1 






L 


F 


R 





Fig. 112. 



imaginary planes and projecting lines have been removed, will 
be a True Drawing or Orthographic Projection of the truncated 
pyramid. 

NOTATION. 

In the drawings illustrating the following problems and 
their solutions the given and required lines are shown wide and 
black. Hidden lines are shown broken into short dashes a little 
narrower than the visible lines. Construction or projection lines 
are drawn with very narrow full or conti?iuous black lines. 



ORTHOGRAPHIC PROJECTION. 8 I 

When convenient very narrow, continuous blue lines are some- 
times used. 

The Horizontal Plane is known as the H.P., the Vertical 
Plane as V.P. and the Profile Plane as Pf.P. 

A point in space is designated by a small letter or figure, 
its projection by the same letter or figure with small h or v 
written above for the horizontal or vertical projection respec- 
tively. 

In some compjicated problems where points are designated 
by figures their projections are named by the same figures 
accented. 

Drawings should be carefully made to the dimensions 
given, the scale to be determined by the instructor. 

The student should continually endeavor to improve in 
inking straight lines, curves, and joints. 

In solving the following problems the student should have 
a model of the co-ordinate planes for his own use. This can 
be made by taking two pieces of stiff cardboard and cutting a 
slot in the center of one of them large enongh to pass the 
folded half of the other through it ; when unfolding this half a 
model will be had like that shown by Fig. 107 or 109. 

All projections shall now be made from the third, 
dihedral angle. 

PROB. 1. — A point a is situated in the third dihedral 
angle, \" below the H.P. and 3" behind the V.P. 

It is required to draw its vertical and horizontal projec- 
tions. 

Draw a straight line a h a v , Fig. 113, perpendicular to I.L. 
and measure off the point a° \" below I.L. and the point a h 
3" above I.L. 



82 



MECHANICAL DRAWING. 



a" is the vertical and a h the horizontal projection in the 
same straight line d°a h . 

The student should demonstrate this with his model. 

PROB. 2. — Draw two projections of a line 3" long parallel 
to both planes, |" below the H.P. and 2" behind the V.P. 

As the line is parallel to both planes, both projections will 
be parallel to the I.L. 

Draw d"b v the vert. proj. of the line 3" long, Fig. 1 14, par- 
allel to I.L. and f" below it. Draw the hor. proj. 2" above 
the I.L. and parallel to it, making it the same length as the 




Fig. 113. Fig. 114. Fig. 115. Fig. 116. Fig. 117. 

vert. proj. by drawing lines perpendicular to I.L. from the 
points a" and b° to a h and b h . 

Prob. 3. — To draw the hor. and vert, projs. of a straight 
line 3" long, per. to the vert, plane, Fig. 115. 

As the line is per. to the vert, plane the vert. proj. will be 
a point below the I.L. and the hor. proj. will be parallel to 
the horizontal plane and per. to I.L. 

PROB. 4. — To draw the plan and elevation of a straight 
line 6" long making an angle of 45 ° with the vert, plane and 
and par. to the hor. plane, Fig. 116. 



ORTHOGRAPHIC PROJECTION. 83 

The plan or hor. proj. will be above the I.L. and make an 
angle of 45 with it. The elevation or vert. proj. will be 
below and par. to I.L. 

Draw from the point a h at any convenient distance from 
I.L. a straight line a h b h 6" long, making an angle 45 ° with I.L. 

Draw a v b v par. to I.L. at a convenient distance below it. 
The length of the elevation or vert. proj. is determined by 
dropping perpendiculars from the end of the hor. proj. a h b h to 
the points a"b\ 

PROB. 5, FlG. 117. — To find the true length of a straight 
line oblique to both planes of projection and the angle it 
makes with these planes. 

a v b v and a h b h are the projections of a straight line oblique 
to V.P. and H.P. Using a" as a pivot, revolve the line a v b v 
until it becomes parallel to I.L. as shown by a v b l v . From the 
point b? erect a per. Through the point b h draw a line par. to 
I.L. cutting the per. in the point b x k . 

The broken line a h b x h is the true length of the line ab, 
and the angle is the true angle which the line makes with 
V.P. 

To find the angle it makes with H.P. : 

Using b h as a pivot, revolve the line b h a h until it becomes 
par. to I.L. as shown by b h af. From the point a x h drop a per. 
Through the point a" draw a line par. to I.L. intersecting the 
per. at the point a?o is the angle which the line ab makes 
with H.P. and the broken line a?b v is again its true length. 

PROB. 6, FlG. 118. — To project a plane surface of given 
size, situated in the third angle and par. to the V.P. 

Let abed be the plane surface 3" long X 2" wide. If 
we conceive lines to be projected from the four corners of the 



84 MECHANICAL DRAWING. 

plane surface to the V.P. and join them with straight lines we 
will have its V. projection a v b v e v d v and shown by Fig. 1 1 8. 
And as the plane surface is par. to the V.P. it must be per 
to the H.P. since the planes of projection are at right angles 
to each other. So the plan or H. projection will be a straight 
line equal in length to one of the sides of the plane surface. 

At a convenient distance above I.L. draw a straight line, 
and from the points a°b v project lines at right angles to I.L., 
cutting the straight line in the points a h b. k The line a h b h is 
the hor. proj. of the plane surface abed. 

PROB. 7, FlG. ii8. — To draw the projections of a plane 
surface of given dimensions when situated in the third angle 
perpendicular to the H.P. and making an angle with the V.P. 

Let the plane surface be 3" X 2" as before and let the 
angle it makes with V.P. be 6o°. 

To draw the plan : 

At a convenient distance above I.L. and making an angle 
of 6o° with it, draw a h b 1 h , Fig. 1 18, 2" long. From b, h drop a 
per. cutting a°b v in the point b" and c°d v in the point d x v , then 
the rectangle a v b 1 v d l v e v will be the vert. proj. or elevation of 
the plane surface abed. 

Prob. 8, Fig. 119. — To draw the projections of the same 
plane surface (1) when parallel to the H.P., (2) when making 
an angle of 30 with H.P. and per. to V.P., (3) when mak- 
ing an angle of 6o° with H.P. and per. to V.P., and (4) when 
per. to both planes. 

Fig. 119 shows the projections; further explanations are 
unnecessary. 

PROB. 9, Figs. 1 19 AND 120. — To draw the projections of 



ORTHOGRAPHIC PROJECTION 



85 



the same plane surface when making compound angles with 
the planes of projection. 

Let the plane make an angle of 30 with H.P., as in the 
second position of Prob. 8, Fig. 119, and in addition to that, 
revolve it through at angle of 30 . First, draw the plane 
parallel to H.P., as shown by a h c h b h d h , Fig. 119, the true size 
of the plane. 




Fig. 119. Fig. 120. 

Its elevation will be the straight line a v b v parallel to I.L. 
Next revolve a v b v , using a v as a pivot, through an angle of 
30 , to the position a v b? , which is its vert. proj. when making 
an angle of 30 with H.P. Its plan is projected in cfb^d*. 

Now as the plane is still to make an angle of 30 with 
H.P. after it has been revolved through an angle of 30 with 
relation to the V.P., its hor. proj. will remain unchanged. 

With a piece of celluloid or tracing-paper trace the hor. 
proj. cfb^df, lettering the points as shown, and revolve the 



86 MECHANICAL DRAWING. 

tracing through the angle of 30 , or, which is the same thing, 
place the tracing so that the line a h c h will make an angle of 
6o° with I.L., and with a sharp conical-pointed pencil trans- 
fer the four points to the drawing-paper and join them by 
straight lines, as shown by Fig. 120. 

And as the line <zV l retains its position relative to H.P. 
after the revolution, its elevation will be found at a v c v , Fig. 
120, in a straight line drawn through a v b v , Fig. 119, intersect- 
ing perpendiculars from #V, Fig. 120. And the vert. proj. 
of the points bfdf will be found at h"d™, Fig. 120, in a straight 
line drawn through b*, Fig. 1 19, parallel to I.L. and intersect- 
ing pers. from b*df> join with straight lines the points 

Draw the projections of the plane when making an angle 
of 6o° with H.P. and revolved through an angle of 30 with 
relation to V.P. 

Draw the projections of the plane when making an angle 
of 6o° with the V.P. and per. to the H.P., Fig. 120. 

PROB. 10. — To draw the projections of a plane surface of 
hexagonal form in the following positions: (1) When one 
of its diagonals is par. to the V.P. and making an angle of 
45 with the H.P. (2) When still making an angle of 45 
with the H.P. the same diagonal has been revolved through 
an angle of 6o°. 

Draw the hexagon i h 2 h 3 h 4 h $ h 6 h t Fig. 121, at any con- 
venient distance above I.L., making the inscribed circle 
= 2%" . This will be its hor. proj. and 2 v a?&\ v its vert, proj., 
the diagonal \ h 2 h being par. to both planes of proj. With 
V as an axis revolve 6 V 4 V 2 V through an angle of 45 °. Through 
the points 2^4/6/ erect pers. to the points 6 1 *5,*4 1 *3 1 * and 2* 






ORTHOGRAPHIC PROJECTION. 



87 



and join them with straight lines. These are the projs. in 
the first position. Now trace the hor. proj, 1*, 2/', etc., on 
a piece of celluloid or tracing-paper and revolve the tracing 
until the diagonal 1*2,* makes an angle of 6o° with the I.L., 
Fig. 122. Next draw pers. from the 6 points of the hexag- 
onal plane to intersect hors. from the corresponding points of 
the elevation in Fig. 121, join the points of intersection with 




straight lines, and so complete the projections of the second 
position, Fig. 122. 

PROB. 11, FIGS. 123 AND 124. — Draw the projs. of a cir- 
cular plane (1) when its surface is par. to the vert, plane, (2) 
when it makes an angle of 45 ° with the V.P., and (3) when 
still making an angle of 45 with the V.P. it has been re- 
volved through an angle of 6o°. 

First position: Draw the circular plane i v , 2 V , y, 4", etc., 
Fig. 123, below the I.L. with a radius = 1}" and divide and 
figure it as shown. 



MECHANICAL DRAWING: 



Since the plane is par. to V.P. its hor. proj. will be a 
straight line i\ 2 h , etc. 

For the second position revolve the said hor. proj. through 
the required angle of 45 to the position a h . . . . 1^, Fig. 123, 
and through each division in i k . . . . a h draw arcs cutting 
a h . . . . i h in points 2 h $ h . . . This is the hor. proj. of the 
plane when making an angle of 45 ° with the V.P. 

The elevation is found by dropping pers. from the points 
in the hor. proj. a h . . .1/ to intersect hor. lines drawn 
through the correspondingly numbered points in the eleva- 




Fig. 123. 



Fig. 124. 



tion and through these intersections draw the elevation or 
vert. proj. of the second position. 

For the third position make a tracing of the elevation of 
the second position, numbering all the points as before, and 
place the tracing so that the diameter y v f° makes the required 
angle of 6o° with the I.L. and transfer to the drawing-paper. 



ORTHOGRAPHIC PROJECTION. 89 

The result will be the elevation of the third position shown 
below the I.L., Fig. 124. Its hor. proj. is found by drawing 
pers. through the points 1, 2, 3,4 ... to intersect hors. drawn 
through the corresponding points in the hor. proj. of the 2d 
position and through these intersections draw the plan or hor. 
proj. of the third position, Fig. 124. 

PROB. 12, FlG. 125. — Draw the projs. of a regular hexag- 
onal prism, 3" high and having an inscribed circle of 4%" 
diam. : (1) When its axis is par. to the V.P. (2) Draw the 
true form of a section of the prism when cut by a plane 
passing through it at an angle of 30 with its base. (3) 
Draw the projection of a section when cut by a plane passing 
through XX, Fig. 125, per. to both planes of proj. 

The drawing of the I.L. may now be omitted. 

For the plan of the first part of this prob. draw a circle' 
with a radius = to 2 T 5 ¥ ", and circumscribe a hexagon about it, 
as shown by a h , b h , b h , etc., Fig. 125. To project the elevation, 
draw at a convenient distance from the plan a hor. line par. 
to a h d ! \ and 3" below it another line par. to it. From the 
points a h b h ^d h , drop pers. cutting these par. lines in the points 
a v b v c v d v , thus completing the elevation of the prism. 

Second condition : Draw the edge view or trace of the 
cutting plane iV> making an angle of 30 with the base of the 
prism, locating the lower end 4' one-half inch above the base; 
parallel to i'4', and at a convenient distance from it draw a 
straight line 1,4; at a distance of 2<f$ n on each side of 1,4 
draw lines 3, 2 and 5, 6 parallel to 1,4, and through the 
points r'2'3'4' let fall pers. cutting these three par. lines in 
the points 1, 2, 3, 4, 5, 6; join these points by straight lines 



9° 



MECHANICAL DRAWING. 



as shown, and a true drawing of the section of the prism as 
required will result. 

For the third condition of the problem : 

Let XX be the edge view of the cutting plane and con 
ceive that part of the prism to the right of XX to be removed 

b c 







From the hor. proj. of the prism draw a right-hand elevation 
or profile proj., and through the points XX draw the lines en- 
closing the section, and hatch-line it as shown. 

Prob. 13.— To draw the development of the lower part 
of the prism in the elevation of the last problem. 



ORTHOGRAPHIC PROJECTION. 9 1 

To the right of the elevation in Fig. 125, prolong the base 
line indefinitely and lay off upon it the distances ab, be, cd, 
etc., Fig. 126, each equal in length to a side of the hex. At 
these points erect pers., and through the points 1*2' $'4! draw 
hor. lines intersecting the pers. in 4, 3, 2, 1, etc. At be 
draw the hex. a h b h b k ^c* ^d* of the last prob. for the base, and 
at 1, 2 draw the section 1, 2, 3, 4, 5, 6 for the top. 

PrOB. 14, FIG. 127. — To draw the projs. of a right cylin- 
der 3" diam. and 3'' long. (1) When its axis is per. to the 
H.P. (2) Draw the true form of a section of the cylinder, 
when cut by a plane per. to the V.P. making an angle of 30 
with the H.P. (3) Draw a development of the upper part of 
the cyl. 

For the plan of the first condition, describe the circle 1' ' , 
2' \ etc., with a radius = ij" and from it project the eleva- 
tion, which will be a square of 3" sides. 

For the second condition: Let 1, 7 be the trace of the 
cutting plane, making the point 7, \" from the top of the cyl. 
Divide the circle into 12 equal parts and let fall pers. through 
these divisions to the line of section, cutting it in the points 
1, 2, 3,4, etc. Parallel to the line of section 1, 7 draw \"j" 
at a convenient distance from it, and through the points 
1, 2, 3, 4, etc., draw pers. to 1,7, intersecting and extending 
beyond \"j". Lay off on these pers. the distances 6 8" — 
6'8', and 5"c/' = 5 '9 ', etc., and through the points 2", 3", 
4", etc., describe the ellipse. 

For the development: In line with the top of the eleva- 
tion draw the line g'g" equal in length to the circumference of 
the circle, and divide it into 12 equal parts a', b' , etc., a', b" , 
etc. Through these points drop pers. and through the points 



02 



MECHANICAL DRAWING. 



I, 2, 3, etc., draw hors. intersecting the pers. in the points 
I, 2, 3, etc., and through these points draw a curve. 

Tangent to any point on the straight line draw a 3" circle 
for the top of the cyl. and tangent to any suitable point on 
the curve transfer a tracing of the ellipse. 

PROB. 15, FlG. 128. — Draw the projections of a right cone 
7" high, with a base 6" in diam., pierced by aright cyl. 2" in 




Fig. 127. 



diam. and 5" long their axes intersecting at right angles 3" 
above the base of the cone and par. to V.P. Draw first the 
plan of the cone with a radius = 3". 

At a convenient distance below the plan draw the elevation 
to the dimensions required. 

3" above the base of the cone draw the center line of the 
cyl. CD, and about it construct the elevation of the cyl., which 
will appear as a rectangle 2" wide and 2%" each side of the 
axis of the cone. The half only appears in the figure. 



OR THO G RA PHIC PR OJE C TION. 



93 



To project the curves of intersection between the cyl. and 
cone in the plan and elevation : Draw to the right of the cyl. 
on the same center line a semicircle with a radius equal that 
of the cyl. Divide the semicircle into any number of parts, 




Fig. 128. 



Fig. 129. 



as I, 2, 3, 4, etc. Through 1, 1 draw the per. A" 1" equal 
in length to the height of the cone, and through A" draw the 
line A" 4" tangent to the semicircle at the point 4, and through 
the other divisions of the semicircle draw lines from A" to the 
line i'V'> meeting it in the points $"2 r, \ 

From all points on the line i'V, viz-. i'VW'* erect 



94 MECHANICAL DRAWING. 

pers. to the center line of the plan, cutting it in the points 
ii //2 i"3i"4i"> anc * with i" as the center draw the arcs 2/ -2, 
3,"-3, 4/ / -4 above the center line of the plan, and through the 
points 2, 3, 4 draw hors. to intersect the circle of the plan in 
the points 2 / 3V> and lay off the same distances on the other 
side of the center line of the plan in same order, viz., 2 / 3 / 4 / . 
Through each of these points on the circumference of the circle 
of the plan draw radii to its center A', and through the same 
points also in the plan let fall pers. to the base of the elevation 
of the cone, cutting it in the points 2 / 3 / 4' ; and from the apex 
A of the elevation of the cone draw lines to the points 2 / 34' on 
the base. Hor. lines drawn through the points of division 2, 
3, 4 on the semicircle will intersect the elements A— 2', A— 3', 
A-4' of the cone in the points 2' 3' ^ \ these will be points in 
the elevation of the curve of intersection between the cylinder 
and the cone. 

The plan of the curve is found by erecting pers. through 
the points in the elevation of the curve to intersect the radial 
lines of the plan in correspondingly figured points, through 
which trace the curve as shown. Repeat for the other half 
of the curve. 

Prob. 16, FlG. 129. — To draw the development of the 
half cone, showing the hole penetrated by the cyl. 

With center 4/', Fig. 129, and element A\' of the cone, 
Fig. 128, as radius, describe an arc equal in length to the semi- 
circle of the base of the cone. Bisect it in the line 4/' 1, and 
on each side of the point 1 lay off the distances 2, 3, 4, equal 
to the divisions of the arc in the plan Fig. 128, and from these 
points draw lines to 4", the center of the arc. Then with 
radii A-a> b, c, d, e, respectively, on the elevation Fig. 128, 



OR THO G RA PHI C PR OJE CTION. 



95 



and center 4," draw arcs intersecting the lines drawn from the 
arc XX to its center 4/'. Through the points of intersection 
draw the curve as shown by Fig. 129. 

PROB. 17, FlG. 130. — To draw the development of the 
half of a truncated cone, given the plan and elevation of 
the cone. 




Fig. 130. 

Divide the semicircle of the plan into any number of parts, 
then with A as center and A 1 as radius, draw an arc and lay 
off upon it from the point 1 the divisions of the semicircle 
from 1 to 9, draw gA. Then with center A and radius AB 
draw the arc BC. iBCg is the development of the half of 
the cone approximately. 



90 MECHANICAL DRAWING. 

PROB. i8,*Fig. 131. — To draw the curve of intersection of 
a small cyl. with a larger. To the left of the center-line of 
Fig. 131 is a half cross-section, and to the right a half eleva- 
tion of the two cyls. 

Draw the half plan of the small cyl., which will be a 
semicircle, and divide it into any convenient number of parts, 
say 12. 

From each of these divisions drop pers. 

On the half cross-section these pers. intersect the circum- 
ference of the large cyl. in the points i', 2', etc. Through 




Fig. 132. 



these points draw hors. to intersect in corresponding points 
the pers. on the half elevation. Through the latter points 
draw the curve of intersection C. 

Prob. 19. — To draw the development of the smaller cyl. 
of the last prob. 

Draw a rectangle, Fig. 132, with sides equal to the circum- 



ORTHOGRAPHIC PROJECTION. 97 

ference and length of the cyl. respectively, and divide it into 
24 equal parts. 

Make AB, 1 i', 3 3', etc., Fig. 132, equal to AB, 1/1", 
2' 2", 3 / 3 // , etc., Fig. 131, and draw the developed curve of 
intersection. 

PROB. 20. — To draw the orthographic projections of a 
cylindrical dome riveted to a cylindrical boiler of given 
dimensions. 

Let the dimensions of the dome and boiler be : dome 
26\" diam. X 27" nigh, boiler 54" diam., plates J" thick. 

Apply to the solution of this problem the principles ex- 
plained in Prob. No. 18, Fig. 131. 

When your drawings are completed, compare them with 
Figs. 133 and 134, which are the projections required in the 
problem. 

Letter or number the drawing and be prepared to explain 
how the different projections were found. 

Prob. 21. — To draw the development of the top gusset- 
sheets of a locomotive wagon-top boiler of given dimensions. 

First draw the longitudinal cross-section of the boiler to 
the dimensions given by Fig. 135, using the scale of 1" = 
1 ft. 

Then at any convenient . point on your paper draw a 
straight line, and upon it lay off a distance AB 35-2" long = 
the straight part of the top of the gusset-sheet G, Fig. 135. 
With center A and a radius = 27-J" (the largest radius of the 
gusset) + 6" (the distance from the center of the boiler to the 
center of the gusset C, Fig. 135) = 33-J", draw arc 1. 

With center i? and a radius — 26§" (the smallest radius of 
the gusset) draw arc 2. Tangent to these arcs draw the 



9 8 



MECHANICAL DRAWING. 



straight line I, 2 extended, and through the points A and 
draw lines I, A and 2, B per. to I, 2. 




Take a point on the per. I, 2, 6 from the point I as a 
center and through the point A draw an arc with a radius 
= 27*". 



ORTHOGRAPHIC PROJECTION. 99 

vVith point 2 as a center and 2B as a radius (26%") draw 
an arc through B to meet the line 1,2. 

Divide both arcs into any number of parts, say 12, and 
through these divisions draw lines per. to and intersecting \A 
and 2B respectively. Through these intersections draw in- 
definite hors. and on these hors. step off the length of the 
arcs, with a distance = one of the 12 divisions as follows: 

On the first hors. lay off the length of the arc A\' and B\' 
=■ Ai and B\ respectively. Then from i' lay off the same 
distance to 2' on the second hors. etc. Through these points 
draw curves Ai^' and Bi2 f . Join points 12' and 13' with a 
straight line Then AB12, 13 will be the developed half of 
the straight part of the gusset. 

On the two ends or front and back of the gusset we have 
now to add \" for clearance + 3I" for lap -f- \" allowance 
for truing up the plates, total = 5 J" '. And to the sides 2%' 
for lap + y allowance for truing up, total = i\" . 

The outline of the developed sheet may now be drawn to 
include these dimensions with as little waste as possible, as 
shown by Fig. 136. Extreme accuracy is necessary in mak- 
ing this drawing, as the final dimensions must be found by 
measurement. 

PROB. 22. — To draw the projections of a V-threaded 
screw and its nut of 3" diam. and f" pitch. 

Begin by drawing the center line C, Fig. 137, and lay off 
on each side of it the radius of the screw \\" . Draw AB 
and 6D. Draw A6 the bottom of the screw, and on AB step 
off the pitch = f", beginning at the point A. 

On line 6D from the point 6 lay off a distance = half the 
pitch = f ", because when the point of the thread has com- 



IOO MECHANICAL DRAWING. 

pleted half a revolution it will have risen perpendicularly a 
distance = half the pitch, viz., ■§■". 

Then from the point 6" on 6D step off as many pitches as 
may be desired. From the points of the threads just found, 

B D 





Fig. 137. Fig. 138. 

draw with the 30 triangle and T-square the V of the threads 
intersecting at the points b . . b . . the bottom of the threads. 

At the point O on line A6 draw two semicircles with radii 

|| the top and bottom of the thread respectively. Divide 

these into any number of equal parts and also the pitch Pinto 

the same number of equal parts. Through these divisions 

draw hors. and pers. intersecting each other in the points as 



ORTHOGRAPHIC PROJECTION. 



101 



shown by Fig. 137, which shows an elevation partly in section 
and a section of a nut to fit the screw. Through the points 
of intersection draw the curves of the helices shown, using 
No. 3 of the " Sibley College Set" of Irregular Curves. 




Fig. 139. 

PROB. 22. — To draw the proj. of a square-threaded screw 
3" diam. and I." pitch and also a section of its nut. 

The method of construction is the same as for the last 
problem, and- is illustrated by Fig. 138. 

PROB. 22. — To draw the projections of a square double 
threaded screw of 3" diam. and 2" pitch, and also a section of 
its nut. 



102 



MECHANICAL DRAWING. 



The solution of this problem is shown by Fig. 139, and 

further explanation should be unnecessary. 

Prob. 23. — To draw the curve of intersection that is 
formed by a plane cutting an irregular surface of revolution. 




Fig. 140. 
Figs. 140, 141, and 142 show examples of engine con- 
necting rod ends where the curve / is formed by the inter- 

tH-tt d: 




Fig. 141. 

section of the flat stub end with the surface of revolution of 
the turned part of the rod. 



OR THOGRA PHIC PROJE CTION. 



I03 



The method of finding the curves of intersection are so 
plainly shown by the figures that a detailed explanation is 
deemed unnecessary. 




Fig. 142. 



SHADE LINES, SHADES AND SHADOWS. 

Shade Lines are quite generally used on engineering work- 
ing drawings; they give a relieving appearance to the projec- 
ting parts, improve the looks of the drawing and make it easier 
to read, and are quickly and easily applied. 

The Shading of the curved surfaces of machine parts is 
sometimes practiced on specially finished drawings, but on 
working drawings most employers will not allow shading be- 
cause it takes too much time, and is not essential to a quick 
and correct reading of a drawing, especially if a system of 
shade lines is used. 

Some of the principles of shade lines and shading are 
given below, with a few problems illustrating their commonest 
applications. 

The shadows which opaque objects cast on the planes of 



104 MECHANICAL DRAWING. 

projection or on other objects are seldom or never shown on 
a working drawing, and as the students in Sibley College are 
taught this subject in a course on Descriptive Geometry, it is 
omitted here. 

CONVENTIONS. 

The Source of Light is considered to be at an infinite dis- 
tance from the object, therefore the Rays of Light will be rep- 
resented by parallel lines. 

The Source of Light is considered to be fixed, and the Point 
of Sight situated in front of the object and at an infinite dis- 
tance from it, so that the Visual Rays are parallel to one 
another and per. to the plane of projection. 

Shade Lines divide illuminated surfaces from dark surfaces. 

Dark surfaces are not necessarily to be defined by those 
surfaces which are darkened by the shadow cast by another 
part of the object, but by reason of their location in relation 
to the rays of light. 

It is the general practice to shade-line the different pro- 
jections of an object as if each projection was in the same 
plane, e.g., suppose a cube, Fig. 143, situated in space in the 
third angle, the point of sight in front of it, and the direction 
of the rays of light coinciding with the diagonal of the cube, 
as shown by Fig. 144. Then the edges a°d v , b v c v will be shade 
lines, because they are the edges which separate the illumin- 
ated faces (the faces upon which fall the rays of light) from 
the shaded faces, as shown by Fig. 144. 

Now the source of light being fixed, let the point of sight 
remain in the same position, and conceive the object to be re- 
volved through the angle of 90 about a hor. axis so that a 



ORTHOGRAPHIC PROJECTION. 



I05 



plan at the top of the object is shown above the elevation, and 
as the projected rays of light falling in the direction of the 
diagonal of a cube make angles of 45 ° with the hor., then with 
the use of the 45 triangle we can easily determine that the 
lower and right-hand edges of the plan as well as of the ele- 
vation should be shade lines. 

This practice then will be followed in this work, viz. : 
Shade lines shall be applied to all projections of an object, 



Fig. 143. 






/ 



\R, 



x- 

/ \ 



\ 



\ 



Fig. 144. 



considering the rays of light to fall upon each of them, from 
the same direction. 

Shade lines should have a width equal to 3 times that of 
the other outlines. Broken lines should never be shade lines. 

The outlines of surfaces of revolution should not be shade 
lines. The shade-lined figures which follow will assist in il- 
lustrating the above principles; they should be studied until 
understood. 



Io6 MECHANICAL DRAWING. 



SHADES. 



The shade of an object is that part of the surface from 
which light is excluded by the object. 

The Cine of shade is the line separating the shaded from 
the illuminated part of an object, and is found where the rays 
of light are tangent to the object. 

Brilliant Points. — " When a ray of light falls upon a sur- 
face which turns it from its course and gives it another direc- 
tion, the ray is said to be reflected. The ray as it falls upon 
the surface is called the incident ray, and after it leaves the 
surface the reflected ray. The point at which the reflection 
takes places is called the point of incidence. 

" It is ascertained by experiment — 

" (a) That the plane of the incident and reflected rays is 
always normal to the surface at the point of incidence ; 

" (b) That at the point of incidence the incident and re- 
flected rays make equal angles with the tangent plane or normal 
line to the surface. 

" If therefore we suppose a single luminous point and the 
light emanating from it to fall upon any surface and to be re- 
flected to the eye, the point at which the reflection takes place 
is called the brilliant point. The brilliant point of a surface 
is, then, the point at which a ray of light and a line drawn to 
the eye make equal angles with the tangent plane or normal 
line — the plane of the two lines being normal to the surface." 
— Davies : Shades and Shadozvs. 

Considering the rays of light to be parallel and the point 
of sight at an infinite distance, the brilliant point on the sur- 
face of a sphere is found as follows: Let A V C V and A h C h y Fig. 



OR 7 "HO G RA PHIC PR OJE CTION. 



107 



145, be a ray of light and A v A h a visual ray. Bisect the angles 
contained between the ray of light and the visual ray as fol- 
lows : Revolve A V C V about the axis A v until it becomes parallel 
to the hor. plane at A v C l v . At C™ erect a per. to intersect 
a hor. through C h at C x h join C?L h (L may be any convenient 




Fig. 145. 



point on the line of vision), bisect the angle L h A h C l h with the 
line A h D\ Join C h L h and through the point D\ draw a hor. 
cutting C h L h at Df, then A h D l h is the hor. projection of the 
bisecting line. A plane drawn per. to this bisecting line and 
tangent to 'the sphere touches the surface at the points 
B°B* where the bisecting lines pierce it. Therefore R'B 11 are 
the two projections of the brilliant point. 



io8 



MECHANICAL DRAWING 



The point of shade can be found as follows: 
Draw A h G, Fig. 145, making an angle of 45 with a hor. 
Join the points E and F with a straight line EF. Lay off on 
A h G a distance equal to EF, and join EG. Parallel to EG 
Fig. 146. Fig. 147. 





Fig. 148, 
draw a tangent to the sphere at the point T. Through T 
draw TP h per. to A h G. From the point P h drop a per. to P\ 
P v is the point of shade. 

Prob. 24.— To shade the elevation of a sphere with graded 
arcs of circles. 



ORTHOGRAPHIC PROJECTION. IO9 

First find the brilliant point and the point of shade, and 
divide the radius I, 2 into a suitable number of equal parts, 
and draw arcs of circles as shown by Fig. 146, grading them 
by moving the center a short distance on each side of the 
center of the sphere on the line B h 2 and varying the length of 
the radii to obtain a grade of line that will give a proper 
shade to the sphere. It is desirable to use a horn center to 
protect the center of the figure. 

Fig. 149 shows the stippling method of shading the 
sphere. 






Fig. 140. Fig. 150. 

PROB. 25.— To shade a right cylinder with graded right 
lines. 

Find the line of light E° by the same method used to find 
the brilliant point on the sphere, except that the line of light 
is projected from the point B h where the bisection line A h D 
cuts the circle of the cylinder. 

The line of shade is found where a plane of rays is tan- 
gent to the cyl. at S v and S h . 

Fig. 150 shows how the shading lines are graded from 
the line of shade to the line of light. 

It will be noticed that the lines grow a little narrower to 
the right of the line of shade on Fig. 150; this shows where 



no 



MECHANICAL DRAWING. 



the reflection of the rays of light partly illumine the outline 
of the cylinder. 

Prob. 26, Fig. 148. — To shade a right cone with graded 
right lines tapering toward the apex of the cone. 

Find the elements of light and shade as shown by Fig. 148, 
and draw the shading-lines as shown by Fig. 151, grading 
their width toward the light and tapering them toward the 
apex of the cone. 






Fig. 151. Fig. 152. 

The mixed appearance of the lines near the apex of the 
cone on Fig. 151 can usually be avoided by letting each line 
dry before drawing another through it, or as some draftsmen 
do, stop the lines just before they touch. 

Prob. 2j. — To shade the concave surface of a section of a 

hollow cylinder. 

Find the element of light 
and grade the shading lines 
from it to both edges as shown 
by Fig. 152. 

Fig. 153* Fig. 153 shows a conven- 

tional method of shading a hexagonal nut. 




ORTHOGRAPHIC PROJECTION. 



Ill 



SHADOWS. 



Let Ry Fig. 154, be the direction of the rays of light 
and C an opaque body between the source of light and a 




Fig. 154. 

surface S. The body C will prevent the rays from passing 
in that direction, and its outline will be projected at D on 
the surface 5. D is the shadow of C. 

The line which divides the illuminated portion of the 
surface 5 from the shadow D is called the line of shadow. 

Shadow of a Point. — If a line is drawn through a point in 
space in a direction opposite to the source of light, the point 
in which this line pierces the plane of projection is the 
shadow of the point on that plane. 



112 



MECHANICAL DRAWING. 



To find the shadow on the H.P. of a point in space in 
the first dihedral angle: 

Let A, Fig. 155, be the point in space, and R the 
direction of the ray of light; then A" is the shadow of the 
point A on H.P., and A H A l H is the hor. proj. and A V A X V the 




Fig. 155. 

vert. proj. of R. B v is the point where R pierces V when 
prolonged below H.P., and B H is its hor. proj. in the G.L. 
The projections of R would then be A V B V and A H B H . 

The shadow of a point in V may be found in a similar 
manner, 

Shadows of Rig J it Lines. — The shadow of a right line on 
a plane may be determined by finding the shadows of two of 
its points and joining these by a right line; e.g., the shadow 
of the line AB, Fig. 156, on H.P. is found as follows: 

Through the points A V B V draw the rays A v A l v and B V B X V 
to intersect the plane of projection in G.L. in the points A* 
and B x v \ from these points drop perpendiculars to meet rays 
drawn through A H and B H in the points A* and B X H . A line 
drawn from A/ 1 to B X H is the shadow of AB on H.P. 

If a right line is parallel to the plane of projection its 
shadow will be parallel to the line itself. 



OR THOGRA PHIC PROJECTION. 



"3 



If a line coincides with a ray of light, its shadow on any 
surface will be a point. 



!_L 




Fig. 156. 

PROB. 28 — To find the shadow of a right line on V.P. 
and H.P: 

Let AB, Fig. 157, be the given line. Find the shadows 




Fig. 157. 



U4 



MECHANICAL DRAWING. 



of the points A and B by passing rays through each of their 
projections to make angles of 45 with G.L. The shadow of 
A H on H.P. is found at A X H , and that of B H at Bf, where the 
rays through these points intersect the H.P. The shadow 
oi A v on V.P. is found at^ r and that of B v at BJ, where 
the rays through these points intersect V.P. Join A X H and 
B* with a straight line and we have the shadow of AB on 
H.P., and the shadow on V.P. is found in the same way by 
joining with a straight line the points ^ r and B t v . 

That part of the shadow which falls on V.P. below G.L., 
and on H.P. above G.L., is called the secondary shadow, 
because it makes a second intersection, i.e., it is conceived 
to have passed through V.P. and made an intersection with 
H.P. behind V.P. With the use of the secondary shadow 
problems like this are easier of solution. 



c v 






j 






h 

r "1 








c "i > 











j \ 




\ 












\d' 




5 




■"^f 




c 




D/ 




A' 






b" 





Fig. 158. 



OR THOGRA PHIC PROJECTION. 



15 



PROB. 29. — A BCD, Fig. 158, is a square plate parallel to 
V.P. ; find its shadow on H.P. 

Through the points A y , B v , D v , and A H C H , B H D r \ draw 
rays making the angle of 45 ° (or any other angle which may 
be adopted) with G.L., and determine the shadows of these 
points as explained in Fig. 155. They will be found in the 
points A"B", C" , D X H . Join these points with right lines 
and they will form the line of shadow of the square plate on 
H.P. 

PROB. 30. — To find the shadow of a cube on V.P. with 
one face in V.P. and the other faces parallel or perpendicular 
to H.P. 

Fig. 159 shows the cube in the given position. The line 
C A DB 




Fig. 159. 
of shade is composed of edges EF> FG, GD, DB, and the 
edges AE and AB in V.P. which coincide with their shadows. 



n6 



MECHANICAL DRAWING. 



The shadow of EF is E V F X , of FG is F x G XJ of GD is G X D X , 
of Z>^ is D X B V . The shadows of the edges AE and .4.5 
coincide with the lines. These shadows are found by the 
same rules used for finding the shadows of a line in Prob. 28. 
The line of shadow is B V D,G X F X F V E V A V D V . The visible line 
of shadow is B V D X G X F X E V C V D V . 

PROB. 31. — To find the shadow of a rectcmgular abacus on 
the face of a rectangular pillar. 

Assume the hor. and vert, projs. of the abacus and pillar 
to be as shown in Fig. 160. 




^ H H 



The line of shade of the abacus is seen to be the edges 
A"B X H and A X H C X H . The plane of rays through edge A X H B X H 
is per. to V.P., and the line A X V E V is its vert. proj. or trace; 
its hor. trace is A X H E H . The shadow on the left side face, is 
vertically projected in the point E x v where the plane of rays 
intersects that face. The ray through the point A X H pierces 
the front face in the point E H y which is the shadow of A X H , 



OR THO GRA PHIC PR OJE C TION. 



117 



and E x H E H y E x v e v is the shadow of the part F H A l H on this 
face. 

The line A X H C" is parallel to the front face, therefore its 
shadow on it will be parallel to itself and pass through E. 

The visible line of shadow is now found to be 1 E^E V H V 2 1. 

PROB. 32. — Construct the shade of an upright hex. prism 
and its shadow on both planes. 

Fig. 161 shows the given prism with its line of shade 




Fig 161. 



A X V B X V E X V D V F V on the vert, proj., C H D H F H E H on the hor. 
proj., and its shadow on both planes. 

PROB. 33. — Given a circular plate parallel to one coordin- 
ate plane ; construct its shadow on the other plane. 



n8 



MECHANICAL DRAWIXG. 



Let A V B V C V D V and A H C H , Fig. 162, be the projections 
of the circular plate. 

Circumscribe a square E V G V about the circle; its shadow 
on H.P. will be the parallelogram A H G H , and the shadows 
of the points A V B V C V D V are projected in the points 




Fig. 162. 

A^B^C^D/ 1 . The shadow of the inscribed circle is an el- 
lipse tangent to the parallelogram at the points A"B^C X H D X H \ 
with B^D^ 1 and A"C" as conjugate diameters. 

The position and length of the axes of the ellipse of 
shadow may be found as follows: 

Erect a perpendicular at the point C v making G V K V equal 
to radius of the circle- draw KOP; then KP is equal to the 
major and MK to the minor axis, and angle 6 is twice the 
angle of the transverse axis with the horizontal conjugate 
diam. ; i.e., KP is equal to 1, 2, MK to 3, 4, and 2, O x C", 
or angle Q y is equal to half KOC v > 



ORTHOGRAPHIC PROJECTION. 



II 9 



PROB. 34. — Find the shade of a cylindrical column and 
abacus y and the shadow of the abacus on the column. 

Let A v B v C v 2ind A H B H C H , Fig. 163, be the projections 
of the abacus, D H E H F H and D H D V G V F H the projections of 
the column. 




G-A 



Fig. 163. 



The line of shade on the column is found by passing two 
planes of rays tangent to the column perpendicular to H.P. 
and parallel to the hor. proj. of the ray of light. KL and 
E H are the traces of these planes tangent to the column at 
the points L, and E H and MN the visible line of deepest 
shade on the cylindrical column. 

The deepest line of shade 1, 2 on the abacus is found in 
the same way. 

The line of shadow on the column of that portion of the 
lower circumference of the abacus which is toward the source 
of light is found by passing vertical planes of rays, as 3, 4, to 



120 



MECHANICAL DRAWING. 



determine any number of points in the line, and joining these 
points by a line as shown in Fig. 163. 

PROB. 35. — Find the shade of an oblique cone and its 
shadow on H.P. 




Take the cone as given in Fig. 164. Pass two planes of 
rays tangent to the cone; their elements of contact will be 
the deepest lines of shade. To determine the elements of 
contact draw a ray through C v \ C X H i»s its hor. trace. From 



ORTHOGRAPHIC PROJECTION. 121 

C" draw lines tangent to the base at D and E; the lines of 
contact are CE and CD y and ECD is the line of shade. 

The visible line of shade on H.P. is E H D H , and on V.P. 
it is C V E V . The shadow on H.P. is E H C, H D H . 

PROB. 36. — To draw a front and end elevation of a rect- 
angular hollow box with a rectangular block on each face, each 
block to have a rectangular opening, and all to be properly 
shade-lined and drawn to the dimensions given on Fig. 165. 

Draw the hor. center line first, and then the vertical center 
line of the end view. About these center lines on the end el- 

Fig. 165. 
A 




Fig. 166. 
evation construct the squares shown and erect the edges of the 
blocks. Next draw the hidden lines indicating the thickness 



122 MECHANICAL DRAWING. 

of the walls of the box and the openings through the blocks, 
measuring the sizes carefully to the given dimensions. 

Draw the front elevation by projecting lines from the va- 
rious points on the end elevation, and assuming the position of 
the line AB measure off the lengths of the hor. lines and erect 
their vert, boundaries as shown by the figure. 

PROB. 37. — Given the end elevation of the last prob., cut 
by three planes A, B and C, Fig. 166. Draw the projections 
of these sections when the part to the left of the cutting plane 
has been removed, and what remains is viewed in the direction 
of the arrow, remembering that all the visual rays are parallel. 

These drawings and all that may follow are to be properly 
shade-lined in accordance with the principles given above. 

ISOMETRICAL DRAWING. 

In orthographic projection it is necessary to a correct 
understanding of an object to have at least two views, a front 
and end elevation, or an elevation and plan, and sometimes 
even three views are required. 

Isometric drawing on the other hand shows an object com- 
pletely with only one view. It is a very convenient system 
for the workshop. Davidson in his Projection calls it the 
" Perspective of the Workshop." It is more useful than per- 
spective for a working drawing, because, as its name implies 
(" equal measures ") it can be made to any scale and measured 
like an orthographic drawing. It is, however, mainly em- 
ployed to represent small objects, or large objects drawn to a 
small scale, whose main lines are at right angles to each other. 

The principles of isometrical drawing are founded on a 
cube resting on its lower front corner, 1, Fig. 167, and its base 



ORTHOGRAPHIC PROJECTION. 



123 



elevated so that its diagonal AB is parallel to the horizontal 
plane. Then if the cube is rotated on the corner 1 until the 
diagonal AB is at right angles to the vert, plane, i.e., 
through an angle of 90 , the front elevation will appear as 
shown at 1, 2, 3, 4, Fig. 167, a regular hexagon. 

Now we know that in a regular hexagon, as shown by Fig. 
167, the lines lA, A$ y etc., are all equal, and are easily drawn 




Fig. 167. 

with the 30 X 6o° triangle. But although these lines and 
faces appear to be equal, yet, being inclined to the plane of 
projection, they are shorter than they would actually be on 
the cube itself. However, since they all bear the same pro- 
portion to the original sizes, they can all be measured with 
the same scale. 

We will now describe the method of making an isomet- 
rical scale. 

Draw the half of a square with sides = 2^" , Fig. 168. 
These two sides will make the angle of 45 ° with the horizontal. 
Now the sides of the corresponding isometrical square, we have 
seen, make the angle of 30 with the horizontal, so we will 



124 



MECHANICAL DRAWING. 



draw 14, 34, making angles of 30 with 1,3. The differ- 
ence then between the angle 2, 1, 3 and the angle 4, 1, 3 is 
1 5°, and the proportion of the isometrical projection to the 
actual object is as the length of the line 3, 2 to the line 3, 4. 
And if the line 3, 2 be divided into any number of equal parts, 
and lines be drawn through these divisions par. to 2, 4 to cut 
the line 3, 4 in corresponding divisions, these will divide 3, 4 
proportionately to 3, 2. 

Now if the divisions on 3, 2 be taken to represent feet 
and those on 3, 4 to represent 2 feet, then 3, 4 would be an 
isometrical scale of j-. 




Fig. 168. 



Since isometrical drawings may be made to any scale, we 
may make the isometrical lines of the object = their true size. 
This is a common practice and precludes the need of a special 
isometrical scale. 

The Direction of the Rays of Light. — The projection of a 
ray of light in isometrical drawing will make the angle of 30 
with the horizontal as shown by the line 3, 2 on the front 
elevation of the hex., Fig. 167. And the shade lines will be 
applied as in ordinary projection. 

PROB. 38. — To make the isometrical drawing of a two- 
armed cross standing on a square pedestal. 



OR THOGRA PHIC PROJECTION. 



25 



Begin by drawing a center line AB, Fig. 169, and from the 
point A draw AC and AD, making an angle of 30 with the 
horizontal. Measure from A on the center line AB a dis- 
tance - T y, and draw lines par. to AC, AD; make AC and 
AD 2%" long and erect a perpendicular at D and C, complet- 
ing the two front sides of the base, etc. 




Prob. 39. — To make the isometrical drawing of a hollow 
cube, with square block on each face and a square hole 
through each block, to dimensions given on Fig. 170. 

As before, first draw a center line, and make an isometrical 
drawing of a 2\" cube, and upon each face of it build the 
blocks with the square holes in them, exactly as shown in 
Fig. 170. 

Prob. 40. — To project an isometrical circle. 

The circle is enclosed in a square, as shown by Fig. 171. 



126 



MECHANICAL DRAWING. 



Draw the circle with a radius = 2" and describe the square 
I, 2, 3, 4 about it. 

Draw the diagonals 1, 2, 3, 4 and the diameters 5, 6, 7, 8 
at right angles to each other. 

Now from the points 1 and 2 draw lines iA, \B and 2A, 
2B f making angles of 30 with the hor. diagonal 1,2. And 




Fig. 170. 

through the center draw CD and EF at right angles to the 
isometrical square. 

The points CD, EF, and GH will be points in the curve 
of the projected isometrical circle, which will be an ellipse. 
The ellipse may be drawn sufficiently accurate as follows : 
With center B and radius BC describe the arc CF and ex- 
tend it a little beyond the points C and F, and with center A 
and same rad. describe a similar arc, then with a rad. which 



ORTHOGRAPHIC PROJECTION. 
{S 



I27 





Fig. 173. 



Fig. 174. 



Fig. 175. 





Fig. 176. 



Fig. 177. 



128 



MECHANICAL DRAWING. 




Fig. 178. 



Fig. 179. 





Fig. 180. 



Fig. 181. 




Fig. 182. 



Fig. 183. 



ORTHOGRAPHIC PROJECTION. 1 29 

may readily be found by trial, draw arcs through the points G 
and H and tangent to the two arcs already described. 

Prob. 41. — To lay off an angle from a corner of the iso- 
metrical cube. 

Construct an orthographic square of any convenient size as 
shown in Fig. 174, and draw the required angle AOB. From 
the corner of the isometrical cube where the angle is to be drawn 
lay off along the side a distance equal to OA of the orthographic 
square and erect a perpendicular at A. Step off the distance 
AB and draw OB the angle required. Any other angle may be 
drawn in similar manner. 

Figs. 177, 178, 179, 180, 181, and 184 are for practice in 
the application of the preceding principles, and at least one 




Fig. 184. 

•of these should be drawn, or it would be better still if the student 
would attempt to make an isometrical projection of his instru- 
ment-box, desk, or any familiar object at hand. These figures 
may be measured with the ij" scale and drawn with the 2" 
scale. 

WORKING DRAWINGS. 

Working drawings are sometimes made on brown detail- 
paper in pencil, traced on tracing-paper or cloth, and then blue- 
printed. 

The latter process is accomplished as follows' 



130 MECHANICAL DRAWING. 

The tracing is placed face down on the glass in the print- 
ing-frame, and the prepared paper is placed behind it, with the 
sensitized surface in contact with the back of the tracing. 

In printing from a negative the sensitized surface of the pre- 
pared paper is placed in contact with the film side of the 
negative, and the face is exposed to the light. 

The blue-print system is almost universal in its application 
to shop drawings, as evidenced in the report on " Conventions " 
found at page 247. 

A Working Drawing in the hands of an experienced workman is 
intended to convey to him all the necessary information as to shape, 
size, material, finish, etc., of a machine or other object that will 
enable him to properly construct it without any additional in- 
structions. This means that it must have a sufficient num- 
ber of elevations, sections, and plans to thoroughly explain 
and describe the object in every particular. And these views 
should be completely and conveniently dimensioned. The 
dimensions on the drawing must of course give the sizes to 
which the object is to be made, without reference to the scale 
to which it may be drawn. The title of a working drawing 
should be as brief as possible, and not very large — a neat, 
plain, free-hand printed letter is best for this purpose. 

Finished parts are usually indicated by the letter '• f," and 
if it is all to be finished, then below the title it is customary 
to write or print li finished all over." 

Working drawings may be divided into three general types, 
viz.: General Plans, Machine Drawings, and Patent Office 
Drawings. 

General Plans consists of foundation drawings, piping draw- 
ings, layout drawings, maps, etc. 



ORTHOGRAPHIC PROJECTION. 131 

Machine drawings include assembly drawings, detail draw- 
ings, diagram and kinematic drawings, sketches and scheming 
sheets. 

Patent Office drawings must conform to the requirements of 
the U. S. Patent Office as published in the " Official Rules of 
Practice." They are generally made on two sheet white bristoi 
board with black ink. Size of sheet io"Xi5" with a one inch 
margin all around. From the top border line of one of the nar- 
row edges ij" at least should be reserved for title, number and 
date. The signatures of inventor, attorney, and witnesses must 
be placed at the bottom of the sheet inside the border line. 



COURSE I. 
PROBLEMS IN MECHANICAL DRAWING 



INCLUDING 



LETTERING, GEOMETRICAL DRAWING, ORTHO- 
GRAPHIC PROJECTION, DEVELOPMENTS, IN- 
TERSECTIONS, AND ISOMETRICAL DRAWING. 



COURSE I. 

MECHANICAL DRAWING. 

MINIMUM NUMBER OF PLATES AND MAXIMUM NUM- 
BER OF HOURS ALLOWED TO COMPLETE EACH 
DIVISION OF THE WORK. 

Note. Registered freshmen conditioned in Mechanical Draw- 
ing will be required to complete satisfactorily the following plates 
in Courses I and II. In Course I, plates i to 6a inclusive, also 
10, ii, 12, 14, 17, 19, and 21 (58 hours). In Course II, plates 22, 
23, 24, 32, 33, 34 and 35 (122 hours). 

Students conditioned in Mechanical Drawing must work at 
least 6 hours per week. 

FIRST SEMESTER. 

Plates i to 6a inclusive, Freehand Lettering, to be handed in 

on or before Wednesday, Oct. 20, 1909. (28 hours.) 
Plates 7 to 10 inclusive, Geometrical Drawing, to be handed in 

on or before Wednesday, Nov. 26, 1909. (22 hours.) 
Plates 11 to 13 inclusive, Orthographic Projection, to be handed 
in on or before Friday, Jan. 29, 1910. (24 hours.) 
Total, 74 hours. 

i35 



136 MECHANICAL DRAWING. 

Students failing to finish any of the divisions within the specified 
time for excusable reasons may make arrangements with the 
Instructor to work in one or more extra periods. 

SECOND SEMESTER. 
Begins Jan. 24, 1910. 

Plates 14 to 16 inclusive, to be handed in on or before' Friday, 

March 4, 1910. (20 hours.) 
Plates 17 and 18, Developments, to be handed in not later than 

Friday, April 1, 1910. (16 hours.) 
Plates 19 and 20, Intersections, to be handed in on or before 

Friday, April 29, 1910. (16 hours.) 
Plate 21, Isometrical Drawing, to be handed in on or before 
Friday, May 20, 1910. (12 hours.) 
Total, 64 hours. 
Total number of hours in first and second semesters, 138 
hours. 

Students failing to complete any of the divisions in the course 
in this semester within the specified time for excusable reasons 
may make arrangements with the Instructor to work in one or 
more extra periods. 

Students doing more than the required number of plates in 
the given time will receive a higher mark, other things being 
equal. 

END OF SECOND SEMESTER. 



PROBLEMS IN MECHANICAL DRAWING. 137 

Directions to be Carefully Observed when Commencing 
Work in Mechanical Drawing. 

students' conduct in class. 

Students will be expected to give strict attention to their 
lettering or drawing work during the full time of each drawing 
period. Materials and instruments must not be put away until 
the warning bell rings. 

Nothing should be brought to the drawing table that is not 
needed for the drawing work in hand. 

If a student expects to be absent from any regular period 
he should endeavor to get excused by the Instructor and make 
arrangements for making up the work. 

A student coming late to class should report at once to the 
Instructor, otherwise he will be marked with an unexcused 
absence. A report from the Instructor concerning the deport- 
ment of each student in class is expected by the Dean every two 
months. 

When a student is absent from class through an unforseen 
cause he should at the next regular period fill out an absence 
blank, giving date and cause of absence, sign it, and hand to 
Instructor. The work of all absent periods must be made up 
by arrangement with the Instructor. 

Plate i. Freehand Lettering, Fig. 185, page 138. — Use the 4H 
pencil sharpened to a long conical point, not too sharp. 

Locate the lower point of the first guide-line 12 squares 
from top and 7 squares from left-hand edge of cross-section pad. 

Guide-lines should be sketched lightly with a downward 
stroke and allowed to remain until letters are approved. 

After drawing the guide-lines for the curved letters, 
analyze the lines of each curved letter, as given on the chart 



i.?8 



MECHANICAL DRAWING. 










3 




CO 

(I 



£ 



PROBLEMS IN MECHANICAL DRAWING. 



1 39 






X 

Q 
si 

1 



Or 






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k 9 



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mw 



140 MECHANICAL DRAWING. 

on the blackboard before attempting to draw the curves 
on the pad. A very close approximation of the first 
curved letter as it appears on the chart should be 
obtained before attempting to draw the second curved 
letter. 

Do not copy the letters or figures on pages 138 and 142, the 
correct form and proportions for all the letters and figures 
must be obtained by a careful study of the chart. 

The work on all the letters and figures must be strictly 
freehand. 

Place at the bottom of each plate at the right-hand corner 
the following information: Plate number, Section (days and 
hours), Time taken to finish plate, and Name, e.g., Mon. 
and Wed., 2-4, Plate 1. Time, 4 hours, Name. The 
height of these letters should be one square high and all 
capitals 

Plate 2. Freehand guide lines must .be drawn for all letters 
and figures higher than one square and allowed to remain 
until letters are approved. 

The same care as to proportion and form should be ob- 
served in lettering this plate as in Plate 1. 

Be careful to balance letters and numbers on all plates 
so that the same space will appear from both ends of line 
to edge of pad. 

The small letters should be extended in width a little be- 
yond the proportion given for the larger letters. 

The open letters should be spaced closely together and 
words should have a liberal space between them, say ij 
squares. 



PROBLEMS IN MECHANICAL DRAWING. 141 



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I Mi! Hi * II 

W fr Q x Q; S > S £ h > Hj tf «; 



Aai 4 III til V * 

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s: 2 



142 



MECHANICAL DRAWING. 




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PROBLEMS IN MECHANICAL DRAWING. 143 

Pencil three words only of the small letters at first and 
submit for criticism before going on with the others. 

Use Ball pen, No. 506, to ink large letters and No. 516 
for small letters and figures. 

Plates 3-6- — in the next three letter plates the directions for 
guide-lines, form, slope, spacing of letters, and for width of 
small letters should be carefully observed. 

Plate 6.* While a substantial majority of the leading 
drafting rooms in the United States are in favor of using Gothic 
Capitals exclusively for notes and titles, there are a number 
using a combination of Gothic Capitals and Lower Case letters. 
So it is deemed wise to introduce one plate of Lower Case letters 
to give the student some knowledge of their form, proportion 
and construction. 

This plate should first be pencilled and after approval, inked. 
In addition to the "Ball" pen, No. 516, for large letters, the 
small letters should be inked with Gillott's No. 303. All pens 
when new should be " exercised" a little before beginning to 
letter. The form and proportion of these letters as given by 
the largest letters in Fig. 190, on page 145, should be adhered 
to as closely as possible. 

In general these letters should be made with down strokes 
of a uniform pressure. The only exceptions are the letters r 

* All letters and figures should have uniform slope. Letters and figures of 
one square high should have a full half square slope. 

Each plate must be signed by Instructor in charge, in pencil before inking and 
in ink when plate is finished. Plates not so signed will be rejected. 

When plates are finished and signed they will be retained by the student until 
the six plates on lettering are completed, when they are to be bound with paper 
binders and handed to the Instructor. 



144 




MECHANICAL , 


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PROBLEMS IN MECHANICAL DRAWING. 



145 




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146 MECHANICAL DRAWING. 

and u. The curved part of the r imay be made with an up stroke 
curved only at the top. The u is made with two down strokes 



S 



1 ■ 

I ! I s A iAl*i*' 

8 * S 8 . § * ft . ^<5! ?k 5 

g i in h |i iH r 

ft * 5^ ^£ S! > 8 ft ° uj ^ ^ ^ 

and the bottom curve filled in with a stroke to the right and upward. 
The m, n, and h should be formed with nearly sharp upper curves. 



PROBLEMS IN MECHANICAL DRAWING. 147 

This plate will have to be repeated until the desired results 
have been obtained. 

Plate 6A, Fig. 191. This is an extra lettering plate for those 
students who may finish the required plates ahead of time. The 
extra plate will increase the grade mark. 



GEOMETRICAL DRAWING, INCLUDING CONIC SECs 
TIONS; ORTHOGRAPHIC PROJECTIONS; DEVELOP- 
MENTS; INTERSECTIONS; ISOMETRICAL DRAWING, 
AND ONE WORKING DRAWING. 

Before beginning the work in Mechanical Drawing read 
carefully the directions given on pages 1 to 17. The size of 
the sheet of cream drawing paper will be i5"X2o". This size 
will be used for all drawings in mechanical and machine draw- 
ing. The border lines and inside divisions will be as shown 
on page 148, except where otherwise directed. 

Use a 6 H pencil sharpened to a long wedge-shaped point, as 
explained on pages 7 and 8. 

The lead in the compasses must also be 6 H and sharpened 
in the same way. A properly sharpened pencil is necessary 
to obtain good work. 

When the work has been completely pencilled with fine sharp 
lines it should be submitted to the Instructor for approval and 
signature, after which the given and required lines of the problem 
are to be repencilled with a strong, bold line, using a 4 H pencil 
sharpened to a conical point (not too sharp). 

Title. The form of title shown in Fig. 192 will be used 
on all drawings and should be pencilled and inked together with 
the border lines whether the drawing is to be inked or not. All 



1 48 



MECHANICAL DRAWING. 



drawings are to be finished pencil drawings, as directed above, 
except where otherwise stated. 



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Following is a list of the problems to be drawn on each 
plate : 



PROBLEMS IN MECHANICAL DRAWING. 149 

Plate 7. (Pages 17 to 26 inclusive.) 

Problems 1, 2, 3, 5, 6, 7, 9, 11, 13, 14, 15, 16, 18, 19, and 
20. Make the dimensions for each problem to suit the given 
space so as to comfortably fill it without crowding. 

Plate 8. (Pages 26 to 35.) 

Problems 21, 22, 24, 25, 26, 29, 30, 34, 35, 37, 39, 40, 41, 
42, and 44. 

Plate 9. (Pages 43 to 53.) 

Problems 54, 56, 57, 58, 59. Use four spaces for problem 
59; 70, 71, 72 and 73 in one space each, 63 in two spaces, and 
94 in one space. 

Plate 10. (Pages 39 to 43.) 

Conic Sections. Divide the plate into nine equal spaces. 
Draw problems 47 and 48 (in problem 48 draw complete upper 
half of ellipse and draw lower half by "Honey's method," prob- 
lem 46), 49, 50, 51, 52, 53, and 55. Make twice the size given 
in the figures. 

Plate ii. (Study pages 74 to 89.) 

Orthographic Projection. Divide sheet into nine equal 
spaces, as shown in Fig. 193, page 150. 

Problem 1 shows three views of a wedge-shaped solid, viz., 
the vertical, horizontal, and profile projections. The vertical 
projection is commonly termed the " Elevation" or "Front 
Elevation;" the horizontal projection is generally called the 
"plan," and the profile projection is known as the "End 
Elevation" or "End View." 



i;c 



MECHANICAL DRAWING. 



It will be seen that the end view is obtained by revolving 
points projected from the plan to the profile plane through an 



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angle of 90 by means of arcs of circles and dropping perpendicu- 
lars to intersect horizontals from the same points in the elevation. 



PROBLEMS IX MECHANICAL DRAWING. 



J 5* 



Problem 2. This is the same solid placed differently and 
having the end view projected by straight lines instead of by 
arcs of circles. This method will be adhered to in preference 
to the other, as it takes less time. 

Problem 3. Given the front and end sections of a rec- 
tangular pyramid ih" wideXi" thickX2 // high. From the given 
views draw the plan. 

Problem 4. Given the plan of a pentagonal pyramid whose 
side is 1", project the front and end elevations. 

Problem 5. Given the plan of an H-shaped block 2" high, 
draw front and end elevations. 

Problem 6. Given the elevations of a + -shaped block, 
draw the plan. 

Problem 7. Given front elevation and plan of a hollow 
rectangular prism, draw the end elevation. 

Problem 8. Given the front elevation of an L-shaped block 
2" long, draw the end elevation and plan. In the title of this 
sheet leave out the word "Details" and make title name "Ortho- 
graphic Projection." 

Plate 12. 

Problem 1. Given the elevation and plan of a 1}" square 
pyramid 1 §" high, draw the end view. 

Problem 2. Given the same pyramid of problem 1 when the 
plan has been rotated to the left through an angle of 15 . Pro- 
ject the front and end elevations. 

Problem 3. Given the front elevation of the figure obtained 
in problem 2 when revolved to the left through an angle of 
1 5 . Draw the plan and end elevation. 

Problem 4. Given the front elevation of problem 1 when 



i5 2 



MECHANICAL DRAWING. 



revolved through an angle of 30 to the right. Draw the plan 
and end view. 

Problem 5. Given the end elevation of the pyramid ob- 
tained in problem 2 when revolved to the right through an angle 
of 1 5 . Project the front elevation and plan. 

PLATE 12. 



H 




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1 



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a 



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33 



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Fig. 194. 

Problem 6. Given the end view of the pyramid obtained in 
problem 3 when revolved to the left through an angle of 45 . 
Draw the front elevation and plan. 

Problem 7. Given the end view of the pyramid obtained in 
problem 4 when revolved through an angle of 30 to the left. 
Draw the elevation and plan. 






PROBLEMS IN MECHANICAL DRAWING. 



J 53 



Problem 8. Given the front elevation obtained in problem 5 
when revolved 30 to the right. Draw plan and end view. 
Title similar to that on Plate 1 1 . 

Plate 13. 

In the same positions as given above draw the projections 
of a rectangular prism, Fig. 199, ii"Xi"X2" high. 





.biG. 201. Fig. 202. 







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Fig. 203. 



Fig. 204. 

Plate 14. 



Fig. 205. 



Using same positions as in Plate 12, draw the projections of 
a hexagonal pyramid, Fig. 197, circumscribed circle of hexagon 
= if" diameter, height if". 



154 MECHANICAL DRAWING. 

Plate 15, 

Given a pentagonal pyramid, Fig. 198, whose side is ij' ; , 
height if", draw the projections of the various positions as 
required in Plate 12. 

Plate 15 B. 

In the same positions as given above draw the projections 
of a triangular prism, Fig. 200, page 153, side of triangle ij", 
height of prism ij". 

Plate 15 C. 

In the same positions as given above draw the projections 
of a T-shaped block, Fig. 201, page 153. 

Plate 15 D. 

In the same positions as given above draw the projections of 
a wedge, Fig. 202, page 153. Plates 15 B, 15 C, 15 D are extra 
plates to be drawn by those who finish the required plates ahead 
of time. 

Plate 16. 

Problem 1. Given the elevation and plan of a hollow tri 
angular prism in the position shown in Fig. 203, page 153. Com- 
plete the projection in the auxiliary plane. 

Problem 2. Given the elevation and end view of a hexa- 
gonal pyramid, draw the projection on the auxiliary plane, shown 
in Fig. 206, page 153. Use same dimensions given in Fig. 197. 

Problem 3. Given the elevation and plan of a wedge, draw 
the projection on the auxilary plane, shown in Fig. 205c page 153. 
Use same dimensions given in Fig. 202. 






PROBLEMS IN MECHANICAL DRAWING. 



J 55 



Problem 4. Given elevation, plan, and revolved position of 
plan of a right circular cone, Fig. 212, page 155. Base 3" diam- 
eter, height 3". Draw elevation and end view in revolved posi- 
tion. See page 88. In planning position of drawings on this plate, 

4 



f 
It 






i 




Fig. 2c6. 



Fig. 207. Fig. 208. Fig. 209. Fig. 210. Fig. 211. 




Fig. 212. 



locate problems 1,2, and 3 along the top of the sheet and problem 4 
in the lower left hand. 

Plate 17. Developments. 

Scheme the layout of all the problems in this plate before 
beginning to draw. 

Problem 1. Given the elevation and plan of a pentagonal 
prism, Fig. 206, page 155, 1" side, if" high, cutting planes A and 
B, draw projections as shown in Fig. 125, page 90. Draw the 
development of the part below the cutting plane B. See Fig. 
126, page 90. 



I §6 MECHANICAL DRAWING. 

Problem 2. Given elevation and plan of a rectangular pyramid, 
Fig. 207, page 155, 2"Xi"Xif" high, and cutting planes A and 
B. Draw projections and developments as required for problem 1. 

Problem 3. Given views and cutting planes of equilateral 
triangular prism shown in Fig. 208, page 155. Draw sections 
and development. 

Problem 4. Given views and cutting planes of pyramid shown 
in Fig. 209, page 155. Draw sections and development. 

In this problem when laying out the development, allowance 
must be made for the unequal inclined edges of the sides of the 
pyramid. See Fig. 117, page 82. 

Plate 18. 

Problem 1. Given the right circular cone, as shown in Fig. 
210, page 155. Draw sectional plan and development. 

Problem 2. Given pentagonal pyramid, Fig. 211, page 155, 
and cutting planes A and B. Draw sections and development. 

Problem 3. Given projections of right circular cone, Fig. 213, 
page 155, and cutting planes A, B, C, and D. Draw the projec- 
tions of conic sections as indicated by center lines. Draw also 
development of part of cone below cutting plane B. If space will 
not permit of full development draw half. See Fig. 130, page 95. 

Plate 19. Intersections. 

Problem 1. Draw three views of two right circular cylinders of 
equal diameter, shown in Fig. 214, page 157, intersecting at right 
angles to each other, Draw curve of intersection. See page 96. 

Problem 2. Make the drawing shown in Fig. 215, page 157, 
and draw curve of intersection. 

Problem 3. Make drawing shown in Fig. 216, page 157, 
and prcjxt curve of intersection. 

Problem 4. Fig. 217, page 157, shows a square prism inter- 



PROBLEMS IN MECHANICAL DRAWING 
Fig. 214. Fig. 215. 



157 



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Fig. 217. 



158 MECHANICAL DRAWING. 

sected by a hexagonal prism partly shown in elevation. Com- 
plete the elevation and draw also half end view. Total length 
of hexagonal prism 4§". 

Plate 20. 

Problems 1 and 2. Construct the curves of intersection 
shown on the connecting-rod ends in Figs. 140 and 141, page 102, 
and draw three complete views of each. 

Problems 3 and 4. Draw the projections of a "V" and 
"Square" threaded screw according to directions given on pages 
99 and 100, Figs. 137 and 138. 

Plate 21. Isometrical Drawing. 

See pages 122 and 123. 

Problem 1. Make the isometrical drawing of a 2 J" cube. 
Draw a 2\" isometric circle on the upper face by the method 
shown in Fig. 171, page 127. From the lower left-hand corner 
of the right-hand face lay off angles of 15 , 30 , and 45 . Use 
method shown in Fig. 174, page 127. See problem 41, page 129. 

Problem 2. Draw the hollow cube as shown in Fig. 170, 
page 126, except that instead of the hollow block on the upper 
face draw a cylinder of if" diameter and 1" high. 

Problem 3. Make the isometrical drawing of a hexagonal 
headed bolt, shank 1" diameter and 2" long. Head 1" thick. 
Use either of the methods shown in Figs. 173 and 175, page 127. 

Problem 4. Make the isometrical drawing of a pentagonal 
prism of i|" sides and 2 J" high. On the top of the prism draw 
an isometric circle of 2" diameter. See Fig. 176, page 127. 

Problem 5. Make the isometrical drawing of the tool box 
shown at Fig. 183, page 128. Dimensions 3 \" long X 2" wideX 1" 
deep, over all. Cover and sides \ ,} thick. Use the method of 



PROBLEMS IN MECHANICAL DRAWING. 



J 59 



offsets shown in Fig. 182, page 128. Place full dimensions on 
this drawing. Plate 21 is to be finished in pencil and inked. 
See directions for inking with the spring bows on page 14, the 



PLATE 22. 



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TWO f£Er AEfE W B£ G/WEM /A/ /AJCMES AFfKCW /-/EADS THUS - A/OT TMUS > 

/?»/?// /nq/cated ar h coiners o/me/vs/oms 



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Fig. 218. 



large compass on page 13, and the ruling pen on page 9. See 
also directions given for inking Plate 22 on page 159. 



Plate 22. Working Drawing. 

Problems 1 and 2. Make the working drawing of connecting 
rod and axle shown in Fig. 218, page 159. Begin by laying off 
the border line and space for title. Draw guide-lines \" high 
and \" space between lines. Locate all center lines of rod and 



t6o 



MECHANICAL DRAWING. 



axle. Use 6 H pencil sharpened as directed on page 8. Draw 
fine, clear, clean-cut lines. When drawings of rod and axle 




are complete and approved, strengthen the lines with 4 H pencil, 
conical point. Then draw dimension lines. Next put in arrow- 



PROBLEMS IN MECHANICAL DRAWING. 161 

heads and dimensions, beginning at the upper left hand and 
working down toward the lower right-hand corner. 

When the drawing is properly finished in pencil and signed 
by the Instructor it will be ready for tracing on cloth. Begin 
the tracing with the spring bow pen. Ink all arcs of circles, 
circles, and irregular curves before inking any straight lines. 
Then ink dimension lines. Next ink arrow-heads and dimen- 
sions in consecutive order, beginning with the left-hand arrow- 
head, then dimension, next sign of inches, and then left-hand 
arrow-head. Ink hatch lines and center lines last of all. For 
weight and character of lines see Standard Lines on page 247. 

Plate 22 F. 

Problem 1. Make drawing of automobile crank axle, as 
shown in Fig. 219, page 160. Use same directions for pencilling 
and inking as given for Plate 22. 

Problem 2. Make drawing of top bracket for planing ma- 
chine, as shown in Fig. 219, page 160. Project also right end 
view of bracket. Make finish pencil drawing and trace on cloth. 

This plate is not required in the course of mechanical draw- 
ing, but credit will be given for it in the Freshman Course to those 
who may have time to finish it in this course. A higher mark 
will be given to the student completing this plate in addition to 
the required plates. 



Course I is preparatory to Courses II and III. 

Course III is given in " Mechanical Drawing and Elemen- 
tary Machine Design," by John S. and D. Reid, John Wiley 
& Sons, New York. 



CHAPTER VI. 

ARCHITECTURAL DRAWING. 

The method of applying the principles of projection to the 
making of architectural working drawings is the same as in me- 
chanical or machine drawings, except that third angle projec- 
tion is used in the latter, while first angle projection is almost 
invariably used in the former. 

The instruments and materials used in architectural draw- 
ing are practically the same as for mechanical and machine 
drawing. There are a few additional materials needed however, 
in architectural work, viz., a tinting brush, water glass, color 
saucer, colors, stick of India ink, slate, ink well, and white draw- 
ing paper suitable for taking water colors. 

While it is true that experienced architectural draftsmen 
use pencils of a much softer grade than those used by machine 
draftsmen, it is better for the student while learning to continue 
the use of the harder grades as required in mechanical 
drawing. 

The following objects which have been selected for problems 
in architectural drawing in addition to those which have been 
given before are necessarily limited. They are elementary and 
preparatory to a larger and more comprehensive course in architec- 
tural drafting. 

162 



ARCHITECTURAL DRAWING. 



I6 3 




164 MECHANICAL DRAWING. 

FRAMING JOINTS. 

In elementary building construction, carpenters' joints occupy 
an important place. The joints are divided into various forms 
of notches, tenons, and mortises and combinations of the same. 

A Single Notch is a hollow cut in a board or scantling into 
which another board is fitted and fastened. Examples of the 
single and double notches are shown in Figs. 220, 221, and 222, 
Plate 23. 

The Butt Joint. — Fig. 223 shows a butt joint where the end 
of a stud is fastened to a plate without a notch. 

End Lap. — Fig. 224 is a special form of double notch usually 
called halving. The boards are of equal thickness and both 
are notched half their thickness, so that when fastened together 
they form a smooth flush surface. 

Beveled Lap. — Fig. 225 is an example of the lap joint when 
the notch in both scantlings is beveled with an equal and opposite 
slope. Fig. 226 shows a lap joint where the pieces cross each 
other. 

Dovetail Halving. — Fig. 227 shows a dovetail lap joint where 
notches are of such slope that the end cannot be withdrawn. 

Mortise and Tenon. — Fig. 229 shows a plain mortise and 
tenon joint. The tenon, A, is the projection on one piece which 
is made to fit into the mortise shown, cut in the other with two 
wedges which are driven in when the tenon is in place to tighten 
it. The shoulders of the tenon are shown at its root; the abutments 
of the mortise are the faces on which the shoulders rest; and 
the cheeks are the two internal faces on which the grain runs 
lengthwise. The tenon is made one-third the thickness of the 
scantling. The finished joint is shown at B. 



ARCHITECTURAL DRAWING 



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mm 



I 



3^> § 111 
<»•$ $ x <tj -vi Q kj 




l66 MECHANICAL DRAWING. 

Mortise and Tenon Joggled Joint. — This joint, Fig. 230, is 
a modification of the preceding one to suit the angle at which 
the timbers are inclined. The left hand end of the tenon is cut 
square to the plane of the abutment to avoid the sharp end which 
would tend to shear the timber beyond. The angle at A should 
be a right angle. An orthographic projection of this joint is 
shown at B. 

Straddle or Bridge Joint. — This joint, Fig. 228, is a reversal 
of the mortise and tenon joint 

Splice or Lap Joint. — Fig. 231 shows a simple lap splice 
used to join two timbers together. 

Scarfed Joint. — Fig. 232 shows a scarfed joint to resist cross 
stress. A fish plate added would strengthen this joint very much. 
The compression part should have a square abutment as shown, 
but the tenon part may have a bird mouth abutment and sally. 

Iron Fish Plate Joint. — Fig. 233 shows the two beams butted 
end to end, and iron fish plates are bolted on to two opposite sides 
and sometimes to all sides for compression. 

BRICKWORK. 

In building a wall with brick the main object is to obtain 
the greatest strength with the materials used, and at the same 
time to obtain the most pleasing external appearance. The 
most important methods used to obtain these results are what 
is known as the English and Flemish bond. By bond is meant 
the connection of bricks' one with another by lapping them over 
each other in building. 

Fig. 234 is an example in English bond where the courses 
appear as heading and stretching courses alternately. 



ARCHITECTURAL DRAWING. 167 

Fig. 235 shows an example of the Flemish bond where the 
headers and stretchers alternate in the same course. 

Brick and Cement Foundations. — The width of the lowest 
course of a wall must be such that it will not press in the ground 
with a greater load per square foot than the ground can safety 
bear. This is accomplished by what is known at footings, whose 
widths should be apportioned to the weight to be carried, so that 
there will be a uniform pressure under all parts of the building. 
An empirical rule is often used which makes the lowest course 
of the footings twice the width of the wall itself. Footings are 
always made in English bond, and spread on each side of the 
wall by one-quarter brick at each off-set. The outer rows should 
be headers as far as possible. 

Concrete is often used nowadays to lessen the pressure per 
square foot on the earth below. Quite often the footings are 
dispensed with, and the wall is built directly on the concrete 
foundation. Fig. 236 shows a sectional elevation of a brick 
footing with a concrete foundation. 

Stone Foundation Wall. — There are three classes of walling, 
viz., rubble, regular course masonry, and ashlar. A proper bond 
is always desirable. This is obtained by using headers and 
stretchers similar to brickwork, but not necessarily so regular. 
Headers are long stones extending into the wall from either face 
and reching beyond the middle of the wall. 

Fig. 237 gives an example of a stone foundation wall. Fig. 
238 regular course masonry, and Fig. 239 rock face, plain and 
chamfered ashlar. 

Fig. 240 shows two segmental arches which have for their 
intrados segments of circles. The names of the different parts 
are given on the drawing. 



1 68 MECHANICAL DRAWING. 

ARCHITECTURAL LETTERING. 

More latitude is allowed to the architectural draftsman in 
his choice of styles of lettering for notes and titles on working 

PLATE 25. 






W" 




















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)H , 


















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Fig. 241. 

drawings than is given o the machine draftsman. The latter 
is required to use that style of letter which gives the neatest 



ARCHITECTURAL DRAWING. 
PLATE 25. 



169 













































































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Fig. 242. 



170 MECHANICAL DRAWING. 

appearance with a maximum of legibility and requires the least 
amount of labor and time to construct it; while the former is 
expected to use a style of letter suggested by the character of 
the drawing to be named and noted. 

The alphabet shown in Figs. 241-242, known as the classic 
Renaissance letters, is selected as a good form of letter for general 
purposes, where a Roman letter would be suitable for the work 
in hand. This alphabet was originally designed by Albrecht 
Durer and adopted by Frank Chouteau Brown, in his treatise 
on "Letters and Lettering," Bates & Guild Company, Boston. 
Mr. Brown's book is recommended to those students who desire 
to follow up their studies in architectural lettering. 

The method used for the instrumental construction of these 
letters is similar to that used in the Roman letter given on page 67. 

For the purpose of learning the form and proportions of 
these letters the alphabet should be drawn mechanically to a 
scale as large as convenient; after which practice should be had 
by forming the letters freehand to smaller sizes, until the student 
becomes familiar with their construction. 



ARCHITECTURAL DRAWING. 171 

ORDERS OF ARCHITECTURE. 

There are, generally speaking, five orders of architecture, 
the Tuscan, the Doric, the Ionic, the Corinthian, and the 
Composite, but in reality there are only three, because the 
Tuscan may be regarded as a simplified Doric, and the Com- 
posite as a Corinthian modified by the Romans in an endeavor 
to surpass the Greeks. (Vignola.) 

Tuscan Order. — Fig. 243 shows the pedestal, base, entablature, 
and capital of the Tuscan order. The dimensions are given in 
inches, but the drawing may be made by using a scale of modules 
given in the figure. 

A module is an arbitrary term for a unit of measure or pro- 
portion partie, or minute, is an arbitrary division of the module. 
Vignola divides the module for the Tuscan and Doric orders 
into twelve parts. 

The technical names given to the different parts are given 
in the figure. 

Doric Order.— Fig. 244 shows the entablature and capital 
of the Doric order according to Vignola, The proportions are 
given in modules and parties. The technical names of some of 
the details are given in the drawing. 

Fig. 245 shows the elevation and plan of the entablature of 
the Doric Order. Fig. 246 gives the complete Order. 

Ionic Order.— In Figs. 247-248 are given the pedestal, base, 
capital, and entablature with some of their details. The propor- 
tions are given in modules. See Prob. 59, page 45, in connection 
with the drawinsr of the volute. 



172 



MECHANICAL DRAWING. 




ARCHITECTURAL DRAWING. 
PLATE 27. 



173 




— JP P&Z~fr 



Figs. 245-246. 



174 



MECHANICAL DRAWING. 




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CHAPTER VII. 
ARCHITECTURAL DESIGN. 

In this chapter are given some notes and suggestions on the 
design and construction of a modern American dwelling house, 
to be followed with the plans and specifications of a concrete 
example showing the practical working drawings prepared by 
Brown Bros., architects, Cedar Rapids, Iowa. 

Each student will be expected to modify this design and pro- 
duce the plans and specifications of a dwelling distinctly different 
in interior arrangement and exterior design, using the given 
drawings as suggestive examples only. 

Sketches. 

When about to prepare drawings of a dwelling for a customer 
the architect must acquaint himself with all the conditions con- 
nected with the problem. 

The location of the lot and its size, the amount of money 
available for the completed house, and the ideas of the customer 
as to number and size of rooms, interior arrangement and exterior 
design, etc. When these are learned he will prepare a sketch 
and submit it for approval, when the sketch for the general 
arrangement and design has been agreed upon. 

Working Drawings. 

The working drawings can be made and the specification 
and contract drawn up ready for signature. When the contract 

*75 



176 MECHANICAL DRAWING. 

is signed the architect will prepare the full-size detail working 
drawings, placing as many as possible on one sheet to facilitate 
the reading of the same by the workmen. 

The scale of \" equal to 1 foot is generally used in making 
the plans and elevations, but of course this varies according to 
conditions. 

SPECIFICATIONS 

FOR ALL LABOR AND MATERIALS REQUIRED IN THE ERECTION AND COMPLETION OF 

A FRAME RESIDENCE 

FOR 

MR. GEORGE M. VERITY, 

TO BE BUILT AT 
MIDDLE TOWN, OHIO. 

ALL WORK AND MATERIALS TO BE IN STRICT ACCORDANCE WITH ACCOMPANYING 

DRAWINGS AND THE FOLLOWING SPECIFICATIONS, PREPARED FOR 

THE PURPOSE BY 

BROWN BROTHERS, 

architects. 

808-9 Security Savings Bank Building, Cedar Rapids, Iowa. 

General Conditions. 

The owner reserves the right to accept or reject any or all 
bids. The work is to be laid out by the contractor, who will be 
responsible for its correctness. A competent foreman is to be 
kept at the building during all working hours to receive and carry 
out the orders given by the superintendent. 

The following specifications and the above mentioned draw- 
ings are intended to correspond and be illustrative of each other, 
and any part of the work that may be mentioned in the specifica- 
tions and not shown on the drawings, or vice versa, is to be executed 
the same as though it had been particularly mentioned and shown 



ARCHITECTURAL DESIGN. 



177 



PLATE A. 




DdSfmrol Moor- Pldfj 



Fig. 249. 



Residence for G. W. Wilson, Champaign, 111., Brown Brothers, Architects, No. 
808-9 Security Savings Bank Bldg., Cedar Rapids, Iowa. 



178 MECHANICAL DRAWING. 

in both. No deviations are to be made from the drawings or 
specifications without the written consent of the owner and 
architect. If any work is, in the opinion of the superintendent, 
executed in a slight or unsound manner, the same shall on his 
orders be immediately pulled down and made right at the sole 
expense of the contractor. None but the most skillful work- 
men are to be employed on the work and any mechanic or laborer 
employed thereon who, in the opinion of the superintendent, 
shall prove careless or incompetent, shall be immediately removed 
therefrom by the contractor when notified to do so by the super- 
intendent. No part of the work is to be done as "piece work," 
nor let to a sub-contractor, without the consent of the owner. 
All materials required for the execution of the work to be fur- 
nished by the contractor, unless otherwise specified, must be 
of the very best quality of their respective kinds, and to be properly 
applied at times as directed by the superintendent. 

All work is to be done in a substantial and workmanlike 
manner, and if any difference of opinion shall arise as to the 
quality or quantity of workmanship or materials or upon any 
other matter connected with the building, the contractor must 
in all cases be bound by the decision of the architect or super- 
intendent. The superintendent may cause to be removed at any 
time before the acceptance of the work any materials or workman- 
ship that does not comply strictly with the requirements of the 
plans or specifications, or in the event that such removal might 
cause damage or injury to the other portions of the work, or if the 
contractor neglects or refuses to remove same, then the architect 
or superintendent may deduct from the amount of the contract price 
a sum that in his judgment shall be just and reasonable as a 
set-off to the injury to the building caused by non-compliance 



ARCHITECTURAL DESIGN. 179 

with the requirements of the specifications, as well as for the 
difference of value between the specified and the inferior work- 
manship or materials, and give his certificate only for the 
balance that may be due the contractor. The architect shall 
have full power to have the work pushed forward, and in default 
of the compliance by the contractor with the terms of a notice 
to that effect within three days of the service of the same, the 
architect shall have full power to enter the premises and entirely 
stop the work, and exclude the contractors therefrom and to 
furnish all materials necessary, or to use materials then on the 
premises, or to employ any other workmen to finish such work 
that may remain unperformed or unfinished, and charge the 
amount of such unfinished or unperformed work to the original 
contractor, with all other expenses or costs that may accrue 
by reason of said change, and to have full power to retain the 
amount of such costs and expenses out of any moneys 
that may then be due or coming due from the original con- 
tractor. 

The contractor shall thoroughly scrape and sweep the floors 
throughout and remove all rubbish from the premises; also see 
that all sash, doors, locks, etc., are in proper working order, 
and shall furnish the proper keys for all locks and leave the entire 
building ready for occupancy. 



Staking Out. 

Contractor must stake out the building, and he must establish 
all levels and pay all charges for engineer, if services of an engineer 
are found to be necessarv. 



180 MECHANICAL DRAWING. 



Bond. 



The contractor will be required to furnish a surety bond 
acceptable to the owner, and be ready to sign contract and execute 
bond within three days after date of the acceptance of his bid, 
bond to be equal to fifty (50%) per cent of the amount of the con- 
tract. A certified check for dollars ($ ) must accompany 

each bid as a guarantee that contractor will sign up at his figures 
within three days after bids are opened, otherwise check is for- 
feited to owner. 

Permits. 

Contractor must obtain and pay for all building permits 
and street permits, and comply with local building ordinance in 
every respect. Proper danger signals must be maintained at 
night and barriers erected to protect the public from accidents. 
Should any accident occur by reason of neglect on the part of 
the contractor, he will be held personally liable for same. 

Excavations. 

Excavate for all walls and piers to a depth as shown on the 
several drawings and sections. All trenches must be of the 
depth as shown, and the bottom of all excavations must be per- 
fectly level before any masonry work is commenced in same. 
All dirt not needed on the premises is to be carried away at the 
expense of the contractor only after having received an order 
to do so from the owner. The grades are shown on the drawings 
and the contractor is to be governed by same in making his calcula- 
tions. In taking the dirt from the main excavations the loam 
is to be stacked in one place and the under soil in another, so 



ARCHITECTURAL DESIGN. 
PLATE B. 



181 



»°j &r* 







M& 



w.J A,, 1 a. 



=^ 



fTr^r fWr PU 



Fig. 250. 

Residence for G. W. Wilson, Champaign, 111. Brown Brothers, Architects, No. 

808-9 Security Savings Bank Bldg., Cedar Rapids, Iowa. 



182 MECHANICAL DRAWING. 

that when grading is done the black loam can be placed on top 
again. All trenches and cellar bottoms are to be thoroughly 
drained of all water before any masonry work is commenced. 
The grading back of dirt that has been thrown out of excavations 
will be done by another contractor or agreed upon with owner 
in this contract. 

Masonry Work. 

All walls, piers, chimneys, etc., in basement and wherever 
shown on plans and elevations are to be of concrete, or of good 
hard-burned merchantable brick, laid in lime mortar, as shown by 
the plans and sections. Submit alternate bid on brick walls. All 
concrete to be made of good Portland cement (Atlas or its equal, 
subject to the approval of the architect) and good coarse gravel 
(or crushed rock in size to pass through a 2" ring) and clean, 
sharp sand. Proportions to be as follows: one part of cement, 
six parts of gravel or crushed rock, and three parts sand. If 
gravel is used in place of crushed rock, omit the two parts of 
sand from mixture. All to be thoroughly mixed dry on a board 
platform and then mixed with water to the proper consistency. 
All concrete must be kept thoroughly wet for at least two days 
after having been placed in the forms. Forms to be made of 
rough plank sides of inch lumber and to be firmly braced and kept 
in place until the concrete has properly set. Build in all pipes 
through concrete walls as work progresses. All exposed face 
brick to be Twin City Brick Co.'s (or its equal) oriental brick, 
Minneapolis, Minn, (medium and dark shades, one-half of each), 
and to be laid up with \" mortar joints and raked out \" deep. 

Build chimneys and fireplaces as shown on drawings, sections 
and details of materials as marked on drawings and line all smoke 



ARCHITECTURAL DESIGN. 



i83 



PLATE C. 



T>oor«, 

Ail 



F-loo^ A'Vn>*i Dint- 







uj «... ~ 



— G)cCOoJ floor H^p-K 



'/ 



Residence for G. W. Wilson, Champaign, 111. Brown Brothers, Architects, No. 
808-9 Security Savings Bank Bldg., Cedar Rapids, Iowa. 



1 84 MECHANICAL DRAWING. 

flues with fire-clay flue linings, All chimney work to be laid 
up with lime mortar with a little cement added. Turn dis- 
charging arches over' each fireplace and support heads of all 
square openings of fireplaces with H. W. Covert's cast-iron throat 
and damper, with four (4) inch bearing on walls at front, back and 
ends. Place thimbles in all chimneys where directed by su- 
perintendent. For design of mantel, see details. Line all fire 
openings with fire-brick laid in fire-clay mortar. 

Cistern. — Provide and put in a 100 bbl. cistern where directed 
by the owner. This cistern is to be built of good hard-burned 
merchantable brick 4" thick, laid in cement mortar for bottom, 
sides and arched top, and to have a \" smooth coat of cement 
mortar (one part cement to one of sand) for the finished surface of 
walls and bottom. 

Cistern is to be circular in plan and to be about 8' in diam- 
eter by the proper height to contain 100 bbls. of water. Provide 
a filter wall on a slight curve in center of cistern, and to extend 
to within 18" of the top. This filter wall is to be laid up of one 
course of brick without any mortar. Provide a cast-iron rim 28" 
in diameter by 6" high to finish off the top, and also provide a 
cast-iron cover with 3" ring. 

Top of cistern cover to be about 12" below finished grade of 
house when completed. Make all proper connections from water 
pipes leading from down spouts to the cistern, and have all pipes 
from down spouts enter cistern wall on same side of filter wall. 
Provide opening in cistern wall to receive the pipe from water 
lift and connection to hot water heater. Provide 6" vitrified 
salt-glazed sewer pipes with cemented joints to connect up with 
all down spouts and cisterns and lay same at least 2' 6" below 
finished grade of house. Provide a fall of at least \" to 



ARCHITECTURAL DESIGN. 1 85 

the foot for all pipes. These sewer pipes are to extend 8" above 
finished grade line at each down spout, and to be thoroughly 
cemented around all spouts. Provide proper overflow pipe to 
cistern and cutoffs for down spouts at ground. 

Water-Proofing of Walls. — Cover the exterior surface of all 
outside basement walls from bottom of footings up to finished 
grade line and over top of wall at this level with one coat of hot 
asphaltum or dehydratine. 

Cement Work. 

Over entire basement floor and wherever marked " cement 
floor" on plans, is to have a cement floor consisting of 3" 
bed of concrete, composed of one part of Atlas Portland cement 
to six parts of crushed rock and three parts of clean, sharp bank 
sand. Top coat to be \" thick, composed of one part of same 
cement as above specified to two parts of clean, sharp bank 
sand, troweled to a perfectly even and polished surface and lined 
off in squares approximately 48X48". 

Lathing. 

All stud walls, partitions and ceilings or first story are to be 
lathed with No. 1 pine, spruce or yellow poplar lath, free from 
red knots or bark, and well seasoned; break joints at least 
every 18". Place lath §" on the ceilings and but very little 
closer on the stud walls. No lathing through the angles 
allowed; all walls to be made solid by the carpenter before 
lathing begins. 

Half green lath are preferred, but if bone dry, wet the lath 
well before plastering. 



i86 



MECHANICAL DRAWING. 



PLATE D. 




-*~^' J y 



rut.. Mitv-.A-s.ju. 

'rw,™*'--., i.l.tb/'iw,. 



fc) 



•r 



Fig. 252. 
Residence for G. W. Wilson, Champaign, 111. Brown Brothers, Architects, No. 808-9 
Security Savings Bank Bldg., Cedar Rapids, Iowa. 



ARCHITECTURAL DESIGN 187 

Plastering. 

Plaster all interior wood lath with " Adamant" patent wall 
plaster (or its equal "Universal,") to be put on according to the 
printed instructions of the manufacturers. Plaster to come to the 
building ready mixed with nothing but the water to be added. 
This is to be two-coat "drawn work," and all walls and ceilings 
are to be given a hard, smooth plaster-of-paris finish in the 
universal white finish (all for papering). 

Use f" grounds around all openings for interior work for 
baseboards, wood strips, etc., in the building. All plaster must 
come up flush with grounds and be roded perfectly straight, true 
and plumb. 

All patching of plastering to be done by the plasterer after all 
woodwork is complete. Plasterer to clean out all his rubbish 
and scaffolding from the buliding when his work is completed. 

Plaster Wainscoating. 

The walls of kitchen, bath and toilets are to have a good patent 
plaster wainscoting — Keene's Best Cement or its equal — 4' 6" 
high; to be two-coat work. First coat to be a scratch coat; 
second coat to be troweled to a perfectly smooth, even and 
polished surface. 

Timbers. — All timbers, girders, trimmers, joists, truss beams, 
partitions, studs, rafters, etc., must be prepared, framed and con- 
structed according to the drawings and sections. All floor joists 
properly sized to widths and jointed, crowning on top edge. 

All "piece stuff" to be clear Georgia, Arkansas or Northern 
pine. 

Joists and built-up girders to be of a size as shown on plans. 

All joists placed sixteen (16) inches on center. 



1 88 MECHANICAL DRAWING. 

All built-up girders to be well spiked together. 

Bridging. — Cross bridging to be made of sound stuff 2 X 2", 
well fitted, put in as soon as joists are leveled, and spiked with 
two iod. nails at each end. Joists from 5 to 8' bearing one row 
12 to 18', two rows of bridging. 

Headers and Trimmers. — To be double thick, well framed 
and spiked together, leaving all openings of sufficient size for 
finish of stairs, chimneys, etc., and in no case closer than 5" 
to the inside of any smoke flue. All openings in brick or 
concrete to have wooden lintels or brick arches, not less than 
4" thick, by the required width to cover the thickness of wall. 
Build in all "wood brick" in brick walls where necessary for 
nailing. 

Partition and Wall Studs. — All studs to be 2X4" set 16" 
on center and doubled and trussed at all openings where re- 
quired, in substantial manner. Partitions to be sized and jointed, 
set plumb and straight. All angles of rooms made double and 
solid. All bearing partitions, and partitions over 6' in length 
to be bridged horizontally once in height. All studding to have 
2 X 4" bearing plates top and bottom. 

Closing up Doors and Windows. — When building is ready 
for plastering, all sash and glass is to be in place, and contractor 
is to have temporary doors and locks for all outside doors. 

Sheathing. — Enclose the entire house, sides and gables with 
D. & M. fence flooring, f X6" yellow pine. Roof sheathing to 
be JX6" S. O. S. No. 2 boards, yellow pine, laid open 2", 
properly nailed to every studding and rafter with two nails to 
the board. Tight sheathing to extend from bottom of studs clear 
up sides of house and into all gables. Open sheathing on roof 
cnly. Fill in between outside studding of bathroom with saw- 



ARCHITECTURAL DESIGN. 



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dust or shavings and pack firm. Cover all sheathing on walls 
and gables with heavy tarred felt paper well tacked on and 
fill in between studs of oustide walls with same felt as above 
specified, so as to leave a double dead air space between 
sheathing and plastering. 

Roof. — The carpenter shall frame and construct, according 
to the drawings, sections and specifications, in the most thorough 
manner, all roof rafters, hips, ridges and valleys. 

Shingles. — Where shown on drawings on roof and sides to 
be first clear red cedar shingles, 5 to 2" and laid 4^" to the weather, 
with two 3d. cut iron nails to each shingle. Make perfectly 
water-tight around all chimneys, skylights, scuttles, etc., gutters, 
fire-walls or wherever the roof of one part joins the perpendicular 
walls of another, with flashings. (See tin and galvanized iron 
specifications.) 

All proper bond timbers, cradles for arches, etc., and wooden 
brick of every description necessary for the proper execution of 
the work to be furnished by the carpenter ; also all lumber necessary 
for lookouts, decks and furring for the tinners, galvanized iron 
work, etc. ; also build all necessary scaffolding to do the carpenter 
work properly. 

Cornice. — All exterior wood finish to be construted in strict 
accordance with details and to be of thoroughly seasoned clear 
cypress. Provide bed mould and beaded ceiling for soffit of all 
cornices. 

Porches. — Build all porches as shown on the plans, elevations 
and details. Use rough posts, timbers, barge boards, brackets, 
casings, etc., for all exterior woodwork except sash, doors and 
frames. Furnish and put in place a 2 J" crown mould all around 
edge of ceiling to finish same against wall. Porch ceilings to 






ARCHITECTURAL DESIGN. 



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192 MECHANICAL DRAWING. 

have "V" edge and center ceiling to be JX6" clear Washington 
fir or cypress. 

Windows. — All windows for this building must be of the forms, 
style and dimensions as marked on plans, elevations, sections 
and details, or as hereinafter described. All pulley stiles to be 
J" thick, of clear yellow pine and provided with best noiseless 
cast-iron ball-bearing axle pulleys (wheels in one solid piece). 
Sash hung to solid braided Silver Lake " A" or " Sampson Spot" 
sash cord and cast-iron weights. Use lead weights where necessary. 
Sash to be of clear seasoned white pine if" thick and to have 
extension ends to side rail of upper sash for all double-hung win- 
dows. 

All casement sash hinged at side to swing out. Screen sash 
on casement windows, hinged at side to swing in. All windows 
to be equipped with Chamberlain's metal weather strips all 
around. 

Frames. — All frames to be made of J" pulley stiles, \" head 
of clear yellow pine, and i f " sills of clear Washington fir or cypress. 
Door frames for outside doors if" thick and rabbetted; same 
material as above. Inside door frames J" thick of same wood 
as finish of rooms, and use wood stops \ XiJ" with moulded 
edge. (See details.) 

Plank Frames. — Basement frames to be of clear cypress or 
Washington fir if" thick. All frames must come to the build- 
ing primed with white lead and linseed oil, one coat. Basement 
window frames to have clear Washington fir or cypress sills 
if" thick. 

Floors. — The first story joists will first be covered with f X 
6" D.&M. fence flooring, yellow pine. Finished floors of living- 
room and dining-room to be quarter-sawed clear yellow pine. 



ARCHITECTURAL DESIGN. 193 

iX2¥' face, T. & G. sides and ends, and no boards to be less 
than 4" long. 

All finished flooring to be first clear JX2^' face, T. & G. 
sides and ends, well secret-nailed to every joint. All other floors 
except as above specified to be clear quartered Arkansas or 
straight-grained Oregon pine, |X4i", T. & G. sides and 
ends. 

Finished floors must be planed and scraped before staining 
or varnishing. All floors must be well protected before varnish- 
ing, until house is entirely completed. Then staining and varnish- 
ing to be done the last thing. No finished floors to be laid until 
all other workmen except painters are through. 

All under floors to be laid diagonally and end joints cut on 
a line parallel with joists, and to lap half the thickness of joists 
and well nailed with two nails to each end of the board and with 
twb nailings on each intermediate joist. 

Porch floors, unless marked "cement" on plan, to be JX4" 
clear-matched Washington fir or cypress, laid in white lead, 
and well drawn up and nailed to every joist. 

Grounds. — Put up grounds for the finish of all windows, doors, 
bases, casings, wainscoting, etc., before plastering. Those on 
wooden partitions to be f X ij"; on brick walls, f X ij". 

Closets. — All closets finished with two shelves to each unless 
otherwise shown on details and plain wood strips extending 
around closets JX4" wide on which to fasten clothes hooks. All 
pantry and kitchen cupboards to have plain doors (no panels), 
f" thick, and to have shelves 12" apart, set on adjustable 
wood strips with cast-iron pin adjusters. Below counter shelves 
provide drawers, bins and doors as marked on plans. All drawers 
to have center oak guide strips underneath. Glass doors to 



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ARCHITECTURAL DESIGX. 195 

cupboards where shown to be AA double strength clear glass, 
put in with wood stops nailed in place. 

Wainscoting. — No wood wainscoting in the building. 

Doors. — All doors must be made of material same as standing 
finish of the rooms in which they occur, thoroughly seasoned, 
and of the sizes marked on plans, fitted in their respective 
places, hung and trimmed complete. All doors, except as otherwise 
shown, to be fine cross panel O. G. stock doors. Xo veneered 
doors in house. 

All cupboard doors to be plain, §" thick (no panels). All 
glass doors to be glazed as shown on drawings, with D. S. clear 
glass unless otherwise marked. Picture mould in all rooms and 
halls except kitchen, bathroom and pantry of same wood as 
other wood finish in the rooms in which it occurs. 

Finish. — All standing finish of living-room and dining-room 
to be clear, quarter-sawed chestnut. All other standing 
wood-work to be clear straight-grained Arkansas or Georgia 
pine. 

All interior finish to be thoroughly kiln dried. (See painting 
specifications for paint and varnishes.) All door and w.mdow 
casings, base, etc., in the several rooms to be the style, form and 
dimensions as per detailed drawings. All casings, bases, etc., 
to lap well over the ground and fit perfectly to the plastering, 
and no finish is to be put up before plastering is thoroughly dry. 
Furnish and put up hardwood corner strips, where required, at 
all exposed plaster angles, of |X2" to extend 5' 6" above 
baseboard, and to have plain square top edges, and to be 
scribed on to baseboard at bottom; corners to be slight rounded. 
Put up rubber-tipped wood base knobs where necessarv for 
doors to swing against, of same wood as finish of rooms. The 



196 mechanical drawing. 

whole to be done in the most substantial and workmanlike manner 
with thoroughly seasoned wood. 

All finish to be first clear, except where otherwise specified. 

All interior finish must come to the building thoroughly 
sanded and ready for the varnish or paint. 

Bathroom Toilet Cabinet. — Build toilet cabinet in bathroom 
where shown; to be the Hess Warming and Ventilating Co.'s 
Sanitary Steel bathroom locker complete (No. 906 Taccma 
Bldg., Chicago, 111.), cased up as directed by architect; to have 
adjustable and movable enameled steel shelves with rounded 
edges, and a plate mirror door. Case to be sunk into wall as 
deeply as possible. Height of case from floor to be as directed 
by owner. 

All interior finish must be absolutely clear and free from 
knots and black spots except where painted, which can have 
spots or dark streaks, but no loose knots or soft places. 

Beam Ceilings.- — All beam ceilings to be as shown on plans 
and details. 

Mantels. — See details for mantel shelves, bookcases, etc., 
all to be same finish as other finish in rooms in which they occur. 
Hearths and face to be Grueby Tile, 6X6", to be selected by 
owner or built of face brick, as described in masonry work above 
grade. 

Hardware. — Contractor is to furnish and put in place all 
nails, strap hinges, pulleys, cord and weights for double-hung 
windows. All finishing hardware will be furnished by owner 
and put on by contractor. 

Glass. — The breakage of glass will be evenly divided between 
the carpenter, painter, plumber, heating man and plasterer if 
party who broke the glass cannot be found. All glass, where 



A RCH i TECT URA L D ESIGN . 



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not otherwise specified, to be AA double-strength glass, well se- 
cured in place. 

All glass where marked "Plate" on plans or elevations to be 
best American Plate ft" thick and absolutely clear. All mirrors 
where shown or described to be ft" plate mirrors, perfectly clear, 
and of a size shown or specified. Use metal track and small 
wheels in lower rail of sliding doors in pantry and kitchen. All 
glass with copper or lead bar muntins to be AA double strength. 

Screens. — (Contractor may submit bid screens of his own make, 
but use same wire and hardware trimming as hereinafter specified.) 

Place Wilier Mfg. Co.'s (Milwaukee, Wis.) or their equal, 
patent screens on all double hinge windows and all outside doors. 
All screen cloth to be best copper bronzed wire, 16 mesh, and 
drawn perfectly tight. 

Casement windows to have screens to cover entire window 
opening and to be hinged at side to swing in room (see details). 
All double-hinge windows to have screens on outside to cover half 
of window and to slide up and down on metal springs and wood 
strips. Inside screen sash to be constructed of same wood as 
finish of rooms in which they occur. All outside screen sash 
for windows to be made of same wood as other exterior finish. 
Front screen door, No. 151, stiles and rails to be made of quarter- 
sawed clear white oak or chestnut, and to be braced with brass 
rod and turnbuckle, also to have spring hinge and rubber-ball 
bumper. Rear screen door stiles and rails of same wood as other 
exterior finish, and to have rubber-ball bumper and brace as above. 
All basement windows to have screens to cover entire window, 
style No. 3, and to be secured in place by metal thumb turns. 

All hardware for screens to be finished by contractor. Use 
two 3X3" butts for casement sash; three 4X4" butts for all 



ARCHITECTURAL DESIGN. 



199 



PLATE I. 



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Fig. 257. 

Residence for G. W. Wilson, Champaign, 111. Brown Brothers, Architects, No. 808-9 
Security Savings Bank Bldg., Cedar Rapids, Iowa. 



200 MECHANICAL DRAWING. 

screen doors; cup catches for all casement screens. All hardware 
for screens on outside to be brass. All hardware for screen on 
inside of building to be steel, plated to match hardware in room. 
Get style of finishes of hardware from the architects. 

The contractor must clear out all lumber, shavings, etc., 
and all other loose rubbish from all rooms in the several stories, 
sweep all floors clean, and remove all rubbish from the premises 
on completion of his contract. All damage to adjoining property 
caused by this contractor to be repaired and left clean and whole 
on completion. 

Tin and Galvanized Iron and Lead Work. 

Down Spouts and Conductor Heads. — All down spouts 
must be well secured to walls, with ornamental galvanized iron 
fasteners, and must extend to ground. Gutters to be made of 
No. 26 galvanized iron and properly graded to down spouts. 
Provide gutters wherever shown to catch water from the roof, 
and provide No. 26 galvanized-iron corrugated down spouts, 
3 X 4", where shown on the drawings, or where necessary to carry 
the water off the roof to ground. Gutters to run up at least 8" 
under shingles. 

All valleys to be lined with 20" N. & G. Taylor's Target 
and Arrow tin. 

Flashings. — Flash around all chimneys, and from roof up into 
brickwork, and counterflash same with tin as above specified. 
Provide substantial galvanized-iron fasteners for down spouts 
where shown. (See details.) 

Iron Work. — Provide the Holland Furnace Co.'s (Holland, 
Mich.) coal window chute for one coal window in basement. 
Also provide all other cast- or wrought-iron work such as ash-pit 



ARCHITECTURAL DESIGN. 



201 



PLATE J. 




Fig. 258. 

Residence for G. W. Wilson, Champaign, 111. Brown Brothers, Architects, No. 808-9 
Security Savings Bank Bldg., Cedar Rapids, Iowa. 



202 MECHANICAL DRAWING. 

doors, frames, etc., and iron throat and damper for fireplace. 
(Covert's Patent Iron Throat and Damper.) 

Guarantee. — The whole of the galvanized iron and tin work 
must be guaranteed for a term of five years. Provide a tin or 
galvanized-iron speaking tube with mouthpieces (one in basement, 
one on first floor, and one on second floor where directed). All 
to be securely fastened to walls and made perfectly tight. 

Painting. 

The contractor must find and provide all the necessary ma- 
terials of every description, including ladders, scaffolding, ropes, 
etc., for the performance of the work in a substantial and workman- 
like manner, and of the best qualities of their respective kinds, and 
clean off all woodwork before priming it. Putty up all nail 
holes, joints, cracks and defects. Sandpaper smooth, and prop- 
erly prepare the same before painting the second coat. 

Priming. — All outside planed woodwork, such as casings, 
sash and frames to be primed as soon as in place with white lead 
and linseed oil. All exterior defects in woodwork must receive 
a strong coat of shellac before priming. All barge boards, posts, 
brackets, etc., to be rough for stain or smooth for paint, as the 
owner may direct. 

Outside Painting. — Paint all the planed woodwork, two (2) 
coats of good white lead or zinc-white and linseed oil, mixed with 
colors to bring it to the shade to suit owner. All side wall and 
roof shingles, also all rough woodwork, and rough siding if any, 
to be given two good brush coats of Cabot's Creosote Shingle 
Stain. (Color to suit owner.) 

Outside doors, if not of hardwood, to be painted two coats 
of zinc white and linseed oil. All outside hardwood doors to be 



ARCHITECTURAL DESIGN. 203 

stained and then given two coats of Pratt & Lambert's spar 
finishing varnish. 

All tin and galvanized iron work to be given one coat of min- 
eral paint, on under side before laying, then two coats of lead and 
oil on finished surface. 

Inside Staining, Painting and Varnishing. — All open-grained 
woods are to receive one coat of paste wood filler (color to suit 
owner) and three coats of Pratt & Lambert's No. 38 preservative 
varnish, lightly sanded between coats. Then one coat of Pratt 
& Lambert's Dulkote. 

All close-grained wood to receive one coat of Pratt & Lambert's 
acid stain (color to suit owner). The two coats of Pratt & Lam- 
bert's No. 38 preservative varnish lightly sanded between coats. 
Then one coat of Pratt & Lambert's Dulkote. 

Tinting. — No ceiling or wall tinting in this job. 

Floor Finish. — All floors except kitchen and bath to receive 
a coat of oil stain to match standing finish and two coats of Pratt 
& Lambert's No. 61 floor varnish. Kitchen and bathroom 
floors to receive a light oil stain and one coat of white grain 
alcohol shellac. 

Picture Molding. — The painter is to finish picture mold to 
match finish of different rooms and of same materials as specified 
for other wood finish in the rooms in which it occurs. 

Plumbing. 

This specification is meant to embrace all the materials 
and labor necessary for a complete system of plumbing, with all 
sewers, supplies, wastes and ventilating pipes for the same. 
All exposed pipes in rooms to be nickel-plated work, except 
where otherwise specified. 



204 



MECHANICAL DRAWING. 




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ARCHITECTURAL DESIGN. 205 

Fixtures. — To consist of goods as specified below, and as 
shown on the drawings. Numbers all taken from Wolff's "H" 
catalogue. (Standard Manufacturing Company's or Mott's goods 
will be accepted, where design, size and quality of goods are 
the equal of Wolff's as specified.) 

Kitchen Sink. — Fig. "H" 8052, to be 18X30". Sink set on 
galvanized -iron sink brackets; supply with hot and cold water 
through two §" N. P. finished Fuller Compression faucets in 
wall over sink, having the "Ideal" centrifugal wastepipe from 
wall to soil pipe, and 1" vent pipe to trap. 

Bathtub— Wolff's Corona roll rim tub, Fig. "H" 6505, 
5' long, first grade enamel finish "Corona," complete, as 
described in catalogue. 

Laundry Tubs. — Wolff's "W" 8158 complete, as described 
in catalogue. Provide wringer holder for these tubs. 

Water Closet. — Where shown on plans, put in Wolff's syphon 
jet "W" 7085 water closet complete, as shown in catalogue. 
Provide the "never-split" seat for water closet. Seat to be cherry 
or birch and finished in ivory enamel. Make all necessary con- 
nections for supply and waste. 

Lavatory. — Furnish and set where shown on plans Wolff's 
Fig. "H" 4050, "The Concord," complete, as described in cat- 
alogue. Make water connections to all fixtures with the city 
mains, and also make proper connections to hot-water pipes 
from heater. 

Water Heater. — Provide and set in basement where directed 
one Ruud automatic gas heater. Make all necessary connec- 
tions to water, vent and gas pipes in strict accordance with 
printed instructions furnished by the manufacturers, and to 
carry hot water to all fixtures except water closet in the 



206 MECHANICAL DRAWING. 

building. Make proper connection to flue for vent where 
directed. 

Contractor to make alternate bid on forty-gallon galvanized 
iron range boiler in kitchen to connect up with waterback in range 
and to all fixtures (except water closet) in the building. 

Sewer. — From outside of wall run 4" iron extra heavy soil 
pipe under house as directed, to connect to all fixtures in the build- 
ing. Continue from outside of house, and run 4" vitrified sewer tile 
below front line with cemented joints to cesspool. Sewer to have 
an even fall of at least \" per foot, and where branches are made 
to different fixtures they must be made with "Y" joints. All 
vent, waste and supply pipes to be size and location as per local 
city ordinance. 

Gas Piping. — Pipe for gas for Ruud heater and to all ceiling 
light outlets where shown on the drawings, using f " pipe. All 
pipes are to be given the peppermint test, and to be installed 
in strict accordance with the local gas company's rules and 
regulations. 

Waste Pipes. — All waste pipes connecting the different fixtures 
to main line of soil pipe are to be of extra heavy lead where they 
are not exposed in the room. All exposed work to be nickel- 
plated pipes as heretofore specified. All wastes below traps may 
be 2" cast-iron soil pipe. Where connections are made to soil 
pipes they must be made by means of brass ferrules. Each fixture 
is to have a separate trap and is to have a separate vent pipe of 
sufficient size run independently through the roof and connected 
on main line of soil pipe at a point at least 2' above the highest 
fixture in the building. 

Water Supply. — The cold water will be taken from city mains 
and cistern through f " galvanized iron pipe, and run in as direct 



ARCHITECTURAL DESIGN. 207 

manner as possible to the different fixtures in the building. Have 
a by-pass system of piping. 

Hot water to be taken from heater in basement, and run to all 
the different fixtures (except water closet) in the building through 
§" galvanized iron pipes. All the above supply pipes are to be 
galvanized iron, except the traps and connections to fixtures, 
which where exposed are to be brass, nickel- plated. Where 
iron and lead pipes are connected together it must be done with 
brass ferrules. All stop and waste cocks for the proper con- 
trolling and draining of these pipes must be provided where directed 
by architects. Make openings in walls of house where shown 
or directed and supply two sill cocks, Wolff's "H" 561 N. P. J" 
with loose key for hose connections as directed. 

Water Lift. — Provide and put in place a "Eureka" water 
lift in laundry where directed and make proper connections to 
city water and cistern for all fixtures. 

All the above materials and workmanship to be first-class, put 
up by experienced workmen under the immediate supervision 
of the plumbing contractor, and when finished to be turned over 
to the owner free from leaks, and perfect in every respect. All 
to be subject to the acceptance of the local plumbing inspector. 
Contractor must furnish certificates of inspection, properly signed, 
before owner's final payment will be given. 

All cellar floor drains are to be placed where directed and to 
comply with city ordinance. 

Cesspool (if no sewer). — Where directed by owner build 
a brick cesspool 8" in diameter and 10" deep (or as deep 
as will be necessary to strike water or sand) with 4" hard-burned 
brick walls laid in cement mortar (no brick in bottom). Arch 
cesspool over at top and provide a cast-iron ring and cover to be 



208 MECHANICAL DRAWING. 

2" in diameter and 12" below finished grade. Connect up 
to sewer in proper manner and trap the sewer just before 
entering cesspool. Contractor to give price ner foot in depth 
over 10". 

Connect the soil pipe under water closet with 4" standard 
cast-iron soil pipe, and continue the same as near as possible 
straight up through the roof, having openings and connections to 
different fixtures. All joints in soil pipe are to be packed with 
oakum, run with molten lead, and thoroughly caulked. No small 
vent pipe shall enter the main vent below the highest fixture in 
the building. 

Electric Wiring. 

General Notes.' — No electric work shall be commenced until 
all plumbing roughing in is finished. All wiring to conform to 
the rules and regulations of the National Board of Fire Under- 
writers. All materials used and all work done must be strictly 
first class. Contractor must furnish certificates of inspection 
properly signed before architect's final certificate will be given. 

Wires. — .ALL wires to be carried to the several outlets as shown 
on plan, such wires to be of sufficient capacity to carry the number 
of lights indicated. All wires must be Habershaw, Okonite or 
Roebling white-core, rubber-covered wires. No splicing of wires 
will be allowed in the walls. 

Switches. — All of the ceiling lights throughout the building, 
unless otherwise specified, shall be controlled on Hart Diamond 
H. push-button switches, located where shown and having plates 
finished to match the hardware of the room in which they occur. 
Place switch at top of cellar stairs to control light at foot of stairs 
in basement. Place switch on the inside of front door to control 



ARCHITECTURAL DESIGN. 209 

veranda light. There must be two switches in dining-room, 
where shown, to control lights in the center fixture. All of the 
bracket lights in the building must be controlled at the fixtures. 
See plans for the number and location of lights and all switches. 

Outlet Boxes.- — At each outlet place a steel outlet box, pro- 
tected with compound to prevent corrosion (ceiling boxes with- 
out covers) , and 4J" diameter, all arranged to permit their being 
placed over gas-pipe outlet. Where no gas pipe is placed, boxes 
to have threaded fixture stubs; outlet boxes to be properly and 
firmly secured in position so that outer edge of box or cover will 
not project more than \" beyond finished plaster. 

Cutout Boxes.- — At point where service enters building place 
a fireproof service cabinet; from this service box run one set of 
three (3) wire mains to cutout box to be placed where directed. 
In service box place a three-pole, single-throw fuse extension 
switch connected to mains, and three service wires of sufficient 
length to reach street wires, which must be connected to fused end 
of switch. 

Cutout boxes to be of steel or cast iron set in wall or parti- 
tions, and furnished with asbestos-lined paneled door to match 
woodwork. In cutout boxes install Edison 3-wire 4-plug cutouts, 
with fused plugs complete. 

Switches. — Each circuit to be provided with a double-pole 
indicating switch. Flush switches to be encased in iron boxes. 

Circuits.- — No more than eight lights are to be on any one 
circuit. 

Capacity of Lights. — Number of light outlets are indicated 
on plans. Wires must be heavy enough to carry one 16-candle 
power lamp for each outlet. 

Bells. — There must be bell in kitchen where directed, to be 



2IO MECHANICAL DRAWING. 

operated from front door push plate. Place floor receptacle and 
extension cord and table push button in dining-room to operate 
buzzer in kitchen. Use Sampson or La Clede batteries for all 
bells, and guarantee same for one year. All push buttons must 
be plated to conform to finish of hardware. 

Telephone.' — This contractor must do all interior wiring or 
telephone. Said telephone having outlets in rear hall or where 
shown on plans. 

Heating. 

We recommend the Spencer Heater, the Capitol Boilers 
and the American Radiator Company's sectional cast-iron 
boiler and their cast-iron radiators. Any one of these heaters 
will be acceptable. Contractors bidding on this work must 
submit a schedule of radiation for each room and give their total 
number of feet of radiation to be used in the house. Also fill 
out their specification printed blanks complete, giving size of 
heater, etc., and submit same to owner along with their bid. 

Contractor is to guarantee to heat house to 70 when coldest 
weather outside. All basement pipes are to be covered with 
asbestos and canvas covering, and all radiators are to be painted 
in colors to suit owner. 

Brown Brothers, Architects, 

No. 808-9 Security Savings Bank Bldg., 

Cedar Rapids, Iowa. 



ARCHITECTURAL DESIGN. 



PLATE L. 



Fig. 263. 




212 



MECHANICAL DRAWING. 



Plate L. Fig. 260 shows the front elevation of a window. 
Figs. 261 to 267 give vertical and horizontal sections as indicated 
in Fig. 260. 

Plate M. Figs. 268 to 273 inclusive, elevations and sections 
of gutters. 

This plate is to be drawn according to directions given under 
" Problems." _ 

Plate N. Figs. 274 and 275 show a Gothic style of lettering 
that is coming into common practice in architectural work 
drawings. 

These plates are to be made according to directions given 
under " Problems." 

In finishing the sections of the woodwork, prepare a dark 
shade of burnt sienna with a very little Chinese ink added and 
draw the wood sections free hand as given in the plate of standard 
sections on page 58. Use a Gillott pen No. 303. 



ARCHITECTURAL DESIGN. 
PLATE M. 



213 




214 



MECHANICAL DRAWING. 
PLATE N. 



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ARCHITECTURAL DESIGN. 
PLATE N. 



2T 5 




CHAPTER VIII. 
SHEET METAL PATTERN DRAFTING. 

Students who have completed Course I in Mechanical Draw- 
ing will find little difficulty in understanding the methods employed 
in solving the sixteen problems included in the following four 
plates of this course. 

Prob. i. It is required to make the pattern drawing of the 
rectangular box made of sheet tin shown by the isometric drawing 
Fig. 276. Fig. 277 shows the elevation and plan in orthographic 
projection and Fig. 278 the developed pattern. The J" width 
added to the end of the sides are bent double as shown in Fig. 276 
and are employed to stiffen the sides. A model of this box may 
be seen in the drafting room. 

Prob. 2 is a conical piece made in two parts of thin planished 
iron. Fig. 279 is an isometrical drawing of the finished piece and 
Fig. 280 the orthographic views. Figs. 281 and 282 show the 
developed patterns with a T V' allowance on the edges for seams. 
See model in the drafting room. 

Prob. 3 requires the drawing of a pattern for a flat-sided 
tapering box shown in isometric at Fig. 283. Figs. 284 and 285 
show the orthographic views and the developed pattern respec- 
tively. The seams are to be soldered, therefore an allowance 

is not necessary in this case. 

216 



SHEET METAL PATTERN DRAFTING. 



217 














218 MECHANICAL DRAWING. 

Prob. 4. Make pattern in one piece of the oblong tapering 
article shown in isometric at Fig. 286. Fig. 287 gives the ortho- 
graphic drawings with dimensions and Fig. 288 the developed 
pattern. Divide the small semicircle in the plan into six equal 
parts. Draw the two center lines, C and D, in Fig. 224, 2}" apart. 
With centers, C and D, and radii r and R draw arcs. From lines, 
C and D, step off on the small arc the divisions found on small 
semicircle in plan. Through the last division draw radial lines 
from C and D and from the latter lay off the remaining side 2J" 
long and add $j" allowance to each end as shown. 

Prob. 5. Make the pattern drawing of a scale scoop assuming 
the two parts of which it is made to be segments of cylinders. 
Fig. 289 is the elevation of the scoop with one edge parallel to the 
horizontal plane, and the corresponding bottom edge making an 
angle of 40 with it. 

Having drawn the scoop as given, draw the outline of the 
cylinders and at the end of the right hand one, draw a semicircle 
equal in diameter to the cylinder and divide the lower quadrant 
into six equal parts marking them 1 to 7. Through these points, 
1, 2, 3, 4, etc., draw lines parallel to the axis of the cylinder cutting 
the upper edge and middle dividing line of the scoop in points 7, 6, 
5, 4, 3, 2, i' and i', 2', 3', etc. respectively. 

In laying out the development, Fig. 290, draw from the point 
7' a line perpendicular to the line 7^7, and at a convenient distance 
from the latter draw the center line 1-1 and on the line f-i in 
both directions, lay off the six divisions found on the semicircle. 
Through these divisions draw lines parallel to 1-1 and intersect 
these with perpendiculars drawn from the corresponding points 
of intersection of the scoop. 

Prob. 6. Draw patterns of scale scoop whose elevation and 



SHEET METAL PATTERN DRAFTING. 



219 






220 MECHANICAL DRAWING. 

end view is shown in Fig. 291. This scoop is similar to that of 
Prob. 1 except that it is formed from the segments of cones. 
Draw the elevation and end view, divide the half of the end view 
as shown and through these divisions draw horizontals to cut the 
line CD. Draw the outline of the complete Cone and from the 
intersecting points on CD draw elements to the apex of the cone. 
With the apex A as center and radius A C draw arc of circle 8- 
8 and lay off upon it from the center line A-i in both directions 
the divisions 1 to 8 found on the end view. 

Where the elements of the cone cut the upper edge of the 
scoop, drop perpendiculars to the contour element of the cone, 
thus finding the true distance of the points from the apex. With 
center A and each of these true lengths as radius draw arcs inter- 
secting the corresponding elements in the development. Through 
these points draw the outline curve of the pattern. 

Prob. 7. Make pattern drawings for a scoop with one end 
funnel-shaped, Fig. 292. The other end is made from the seg- 
ment of a cone exactly like Prob. 1. 

The funnel-shaped end is made from a cone, therefore the 
methods used in Probs. 1 and 2 can be applied here without any 
further directions. 

Prob. 8. Draw pattern of grocer's scoop, Fig. 293. The 
body of scoop is cut from a cylindrical form as in Prob. 1. The 
methods are clearly shown in the drawing. Fig. 294 is the 
pattern of the body. 

The handle is made up of two cone frustrums and the con- 
struction is similar to that used in Prob. 2. Figs. 295 and 296 
are the handle patterns. 

The student should be able to lay out these patterns without 
any further assistance. 



SHEET METAL PATTERN DRAFTING. 221 

TRIANGULATION. 

Many articles in sheet metal work are of such irregular form 
that the methods employed in the preceeding problems cannot 
be used. It is therefore necessary under such conditions to obtain 
the development by measuring the whole surface part by part by 
means of triangles. Fig. 297 will illustrate the method of measur- 
ing the surface of an article of irregular form by means of triangles. 
If the article is symmetrical about its axis it will only be necessary 
to divide a quadrant of the top and bottom each with the same 
number of equal parts. Fig. 297 is an isometrical drawing of 
the irregular figure shown in Fig. 301. The quadrant 1 — 5 is 
divided into four equal parts, top and bottom. Join 1 — i", 
2-2", 3-3", 4-4" and 5-5". Also join 1-2', 2-2', 2-3', 
3 — 3', 3 — 4' 4 — 4 f , 4—5' an d 5— 5 r . These latter lines are the 
projections of the lines 1 — 2", 2 — 2 r/ , 2—3", $ — $", 3 — 4", 4 — 4", 
4— 5", and 5 — 5" and are used as the bases for the triangles laid 
out at Fig. 302 to find the true length of the lines joining the points 
in the top and bottom quadrants, for example i' — 2', in Fig. 302 
is the true length of 1 — 2' on the plan of Fig. 301 ; 2"— 2, Fig. 302, 
is the true length of 2' — 2 in plan of Fig. 301, etc. 

In laying out the development, Fig. 303, 1 — i' is taken directly 
from the elevation, Fig. 301, because it is in its true length being 
parallel to the vertical plane. The next step is to take i'— 2 , Fig. 
301, as a radius and i', Fig. 303, as center, desrcibe an arc 1'— 2', 
then with i'— 2', Fig. 302, as radius and 1, Fig. 303, as center, 
describe arc putting arc 1 — 2' in the point 2'. With 1, Fig. 303, 
as center and 1 — 2, Fig. 302, as radius describe arc 1 — 2, Fig. 303, 
and with 2', Fig. 303, as center and 2"— 2, Fig. 302, as radius 
describe arc cutting arc 1 — 2 in the point 2 and so on, determining 



222 



MECHANICAL DRAWING. 




SHEET METAL PATTERN DRAFTING. 223 

the remaining points, 3, 4, 5, and 3', 4', 5' ji Fig. 303 ji the same 
way. The remaining part of the semi-development 5 — B, Fig. 
303, is a duplicate of that already found. 

Prob. 9. It is required to make a pattern drawing for the 
article of irregular form shown in Fig. 298. Draw the plan and 
elevation as given and divide the upper and lower half into the 
same number of equal parts. Lay out the triangles, Fig. 299, and 
determine the development of the left quarter in the same manner 
as described above in reference to Fig. 297. 

The right half of Fig. 298 is the half of a truncated cone, so 
that the development of that part is quite simple. Produce the line 
8 — 8' in the elevation, Fig. 298, to C, the apex of the cone, and 
when 5 — 5 y , Fig. 300, has been drawn, produce it and layoff upon 
it from 5, 5 — C equal to 8 — C in Fig. 298. With C as center and 
C — 5' and C f — 5 as radii describe arcs 5' — 8' and 5 — 8 respec- 
tively, and complete the semi-development. 

Prob. io. Draw the pattern for the article of irregular form 
shown in Fig. 301. Sufficient directions for the solution of this 
problem were given in reference to Fig. 297. 

Prob. ii. Make the pattern drawing for the coal scuttle shown 
in Fig. 304. Draw the elevation and plan as given. Observation 
will show that the form of the scuttle from 1 — 5 is part of a cone, 
so its development can be easily accomplished. The remaining 
portion will be developed by triangulation. 

Lay out development as follows: with r and r + a, Fig. 304, 
as radii describe arcs 1 — 4 and i'— 5', Fig. 305. On the curve 
i' — 5', Fig. 305, lay off the points 2', 3', 4', from the divisions of 
the small circle in the plan, Fig. 304. Through these points draw 
radial lines from C and make a' b' c f a' e' equal in length to abce 
of the elevation, Fig. 304, and thus determine the points 1, 2, 3 



224 MECHANICAL DRAWING. 

4, 5, Fig. 305. Through the points found draw curve as shown. 
To determine points 6 and 7 construct the three triangles shown 
in Fig. 306. Then with center 5', Fig. 305, and 5' — 6', Fig. 304, 
as radius describe arc and with point 5, Fig. 305, as center and 
5" — 6', Fig. 306, as radius describe arc intersecting at 6'. With 5, 
Fig. 305, as center and 5 — 6, Fig. 304, as radius describe arc and 
with 6', Fig. 305, as center and 6' — 6 as radius describe arc inter- 
secting at point 6. With the latter point as center, and 6 — 7 
from the plan as radius describe arc, and with 6' as center and 
6'— 7' from the plan as radius describe arc. With 6, Fig. 305, as 
center and radius 7"— 7', Fig. 306, draw arc intersecting at 7'. 
With the latter point as center and f— 7 from the elevation as 
radius draw arc intersecting in 7. Complete the development 
by joining 6—7 with a straight line and join 5 and 6 with an arc 
of a circle with radius equal to 5 — 6. Join 5', 6' and f with an 
irregular curve. Develop the pattern for base. 

Prob. 12. Draw patterns for bath tub given in plan and 
elevations in Fig. 307. 

Draw plan, elevation, half-right end elevation and half-left 
end elevation in the order named. Draw also a half-lett end 
view from plan in first angle projection. The half pattern of the 
body may be developed at once by the method of parallel lines. 
Divide the left end view of tub i^to 4 equal spaces 1, 2, 3, 4, 5, 
and step these distances off on the line ab of the development and 
draw through the points parallel lines. From the points 6, 4, 
3, 2, 1 of the elevation drop perpendiculars to intersect the cor- 
responding lines in the development at 1, 2, 3, 4, 5, add 5, 6, and 
complete the half deveolpment of the body. The half development 
of the warped surface of the foot can now be obtained in the follow- 
ing manner : Divide the quarter circle of the corner in the plan in- 



SHEET METAL PATTERN DRAFTING. 225 

to 4 equal parts in the points 2', 3', 4', 5', 6', and project these 
points to the line i' — 6 of the end view. Project the points 1, 2, 
3, 4, 5 to the curved line of the end view. Lay out the triangles 
to obtain the true lengths of the measuring lines. The heights 
are obtained from the end view at A, the bases from the plan. 
The true lengths of the upper edge of the pattern are taken from 
the plan while the radii for the respective arcs of the lower edge 
must be taken from the outline of the pattern for the body : Thus 
the radius 1 — 2, Fig. 309, is taken from 1 — 2, Fig. 308, and so on. 
The radius 1 — 2', Fig. 309, is taken from 1 — 2' in (^4), 2 — 2' in 
Fig. 309 from 2 — 2 (B), 2 — 3' in Fig. 309 from 2" — 3' in (B) and so 
on. The development of the pattern of the head piece is found in 
a similar way. The line 1 — 1', Fig. 310, can be taken directly from 
1 — 1' in the elevation as it is shown there in its true length. To 
find the true lengths of the remaining lines the heights of the 
triangles are laid off on the line 1/— 2' from the respective lines 
in the plan, for example i'— 2' is equal to 1'— 2 in the plan and 
so on. The bases of the triangles are projected from the end 
view in 6, 5, 4, 3, 2, 1, and each hypothenuse drawn in order. 
The arcs 1 — 2, 2 — 3, etc., and 1'— 2', 2' — $', etc., are taken from 
the corresponding distances in the plan. The development 
may now be completed by drawing arcs, using each hypothenuse 
of the triangles in their proper order as radius. 

Prob. 13. Draw the development for a two-piece pipe elbow, 
Fig. 311. 

Draw the plan and elevation to the dimensions given and 
develop the half of one piece by the method shown. The 
methods used in finding the developments in this plate are so 
clearly shown that the student should not require any detail 
directions. 



226 



MECHANICAL DRAWING. 




SHEET METAL PATTERN DRAFTING. 227 

Prob. 14. Develop the necessary patterns for a three-piece 
elbow. Fig. 312. 

Prob. 15. Develop the necessary patterns for a five-piece 
elbow. Fig. 313. 

Prob. 16. Draw the pattern of a two-piece oblong pipe elbow. 
Fig. 3 T 4. 



CHAPTER IX. 

ELEMENTARY MACHINE DETAILS, INCLUDING SCREWS, NUTS, 
BOLTS, KEYS, COTTERS AND GIBS, COUPLING SPRINGS, ETC. 



A Screw is a helical projection or thread formed upon a 
cylinder and is the most common device used in mechanical 




Fig. 315. 

combinations. It is employed in the construction of machinery 

for producing pressure contact and transmitting motion. WheD 

228 



ELEMENTARY MACHINE DETAILS. 22Q 

the thread of an external screw is made to fit into the corre- 
sponding hollow of an internal screw (Fig. 315) the latter is 
termed ts nut. 

The Pitch of a Screw-thread is the lineal distance its 
nut would advance along the axis in one turn. In a single- 
threaded screw the pitch is the distance between the centres 
of two consecutive threads measured in the direction of the 
axis, in a double-threaded screw it is the distance from 
centre to centre of every alternate thread, and in a triple- 
threaded screw it is a distance that will embrace three threads. 
For screw-fastenings, instead of giving the pitch the number 
of threads per inch of screw is given — for example, a bolt 
of \" diameter has generally 8 threads per inch; this means 
that the bolt has a single thread wound around it 8 times for 
every inch of its length. 

Right- and Left-handed Screws. — Screws are made 
right- and left-handed, of which the right-handed are the 
more common and are distinguished by their nuts advancing 
along the screws when turned in the direction in which the 
hands of a watch revolve. On a drawing the right-handed 
screws are distinguished by the threads inclining upwards 
towards the right hand when the screws are in a vertical 
position, as in Fig. 315. When a nut with a right-handed 
thread is shown in section the direction of the threads in the 
nut is the opposite to the threads on the screw. 

The Nominal Diameter of a Screw is the diameter over 
the tops of the threads and is equal to the diameter of the 
cylinder upon which the thread is cut. It is the area of the 
nominal diameter that is considered when estimating the 
shearing strength. 



23° 



MECHANICAL DRAWING. 



The Effective Diameter is the diameter at the bottom 
of the thread and is equal to the diameter of the hole in the 
nut before its threads are cut. Unless when the bolts are 
subjected to a shearing stress, it is the area of the effective 
diameter that is considered in estimating their strength. 

The Depth of the Thread is the distance measured 
perpendicularly to the axis of the screw from the top to the 
bottom of the thread. 



NOTATION. 
d= nominal diameter of bolt; 
d=- effective diameter of bolt; 
d = depth of thread ; 
S x — total depth of V; 
p = pitch of thread ; 
n = number of threads per inch. 
The Forms of Screw-threads in general use in machine 
construction are represented in Figs. 316-320. The V thread 
is adopted on all screw-fastenings because of the shearing 
strength of the threads and frictional holding power, which 
is due to the normal pressure on the thread being inclined 
\^..V >J p 




Fig. 316. 
to the axis of the screw. This normal force N, Fig. 316. 
may be resolved into two components, one L parallel to the 



ELEMhNTARY MACHINE DETAILS. 231 

axis of the screw, and the other R at right angles to it. 
L represents the load carried by the thread and R the force 
tending to burst the nut ; therefore the greater the angle 
of the V the greater will be the normal component or 
bursting force, and, the friction being proportional to the 
normal force, it will increase with the angle of the V. Of 
the forms of V threads shown two (Figs. 316 and 317) are in 
common use in the United States for bolts and nuts. 

The Sellers or United States Standard, a section of 
which is shown in Fig. 316, has been adopted by the U. S. 
Government, the Railway Master Mechanics' Association, the 
Master Car-builders' Association, and many of the principal 
manufactories in this country. The sides of this thread 
form an angle of 6o° with each other, and are \ of S x short of 
meeting at a sharp point at the tops and bottoms, which 
makes the sides of the thread in length equal to } of the 
pitch, and the depth of thread S will be expressed by the 
formula 

d = £ X p sin 6o° = 0.65/ (i) 

The effective diameter will then be 

d, = d — 26 =d — i.^p = d — l -^-. . . (2) 

n ' 

The relation between the pitch and the diameter will be ex- 
pressed by the formula 



p = 0.24 |/V_j_ 0.625 -0.175. . . . (3) 
The number of threads per inch is 

n = - = — . . . (4) 

p 0.24 s/ d + .6 25 -0.175 



232 



MECHANICAL DRAWING. 



The table of proportions on page 70 has been deduced from 
the preceding formulae. A difference, however, may be found 
between the formulae and the table in the number of threads 
per inch, as the table has been modified to avoid as far as 
practicable troublesome combinations in the gears of screw- 
cutting machines. 

Exercise 1. — Draw 6 threads in sectional outline, of the 
Sellers thread (Fig. 316), suitable for a screw 6" in diameter. 
Scale three times full size. 

Construction. — Begin by drawing a horizontal line in the 
upper left-hand corner of the paper £■" down from the border- 
line, and a vertical line about f " in from the left-hand border- 
line. Then find the pitch p by the formula (3), and from 
where the two lines you have just drawn intersect mark off 
with the scale on the horizontal line 6 points a distance 
apart equal to the pitch as found by the formula. Through 
these points with the 30 triangle draw the Vs. Complete 
the pencilling by dividing the depth of the V into 8 equal 
divisions, and cut off one division at the top and bottom of 
each thread. 

The Sharp V Thread, shown in Fig. 317, is one of the 

\ — p—A 




Fig. 317. 
forms of threads that were in use before the Sellers thread 



ELEMENTARY MACHINE DETAILS. 233 

was adopted as the U. S. standard, and is still used, although 
condemned by all progressive engineers. This thread is the 
■same as the Sellers thread except that the sides are made to 
meet at a sharp point at the top and bottom, which makes 
the sides of the thread equal in length to the pitch/, and 
the depth of the thread 8 X will be expressed by the formula 

6 X = / sin 6o° = 0.866/ (5) 

The effective diameter of the bolt (d } ) will then be expressed 
by the formula 

d x = d — 2 X o.866>= d— 1.732. . . (6) 

Now, comparing the effective diameters, we have: 

U. S. threads d l = d — i.$p (2) 

V threads ^ = ^—1.732/ (6) 

This serves to show that with an equal pitch the effective 
diameter of the screw having a U. S. standard thread is 
greater than one with a sharp V thread. While the latter form 
of thread materially diminishes the strength of the bolt, the 
sharp point adds very little strength to the thread. A fur- 
ther objection to this form of thread is the variation in depth 
of the threads due to the wear of the sharp points on the taps 
and dies used in producing them. 

The Whitworth V Thread, an outline section of which 
is shown in Fig. 318, is the British standard, and is generally 
adopted on all screw-fastenings in British machine construc- 
tion. It has the sides of the V inclined to each other at an 
angle of 55 , and has an amount rounded off at the top and 
bottom equal to \ of the total depth of the V. The table oj 



2 34 



MECHANICAL DRAWING. 



dimensions for Whitworth screws (page 70) has been deduced 
from the following formulae. The total depth of the V 

d i= = 0.5 cot 27i° = 0.96/ (7) 

1 




Fig. 318. 

The depth of the finished thread 

S = I X 0.96/ = 0.64? (8) 

The pitch / = o.oZd +0.04 (9) 

Number of threads per inch 



1 , I 

= — and p = — 

p r n 



(10) 



The diameter at the bottom of the thread will be given by 
the formula 

1.28 



</,=^-2X O.64/ = d — 



(II) 



Exercise 2. — Draw 6 threads of the Whitworth form of 
thread (Fig. 318). Pitchy. Scale three times full size. 

Construction. — At a suitable distance below the drawing 
of the Sellers thread draw two horizontal lines parallel to 
each other and a distance apart equal to 0.96/. On the 
upper line mark off a distance ab equal to the pitch. Bisect 



ELEMENTARY MACHINE DETAILS. 235 

ab and draw the bisecting line to cut the lower parallel line 
at the point c. Join ca and cb, which will be inclined to each 
other at an angle of 55 . Mark off the pitch from b along 
the upper line, and from c along the lower line, to give the 
required number of threads. Complete the pencilling by 
rounding off the sharp points of the V. 

The Square Screw-thread. — The form of thread which 
is invariably called the square thread is really a rectangle, 
the depth of the thread being equal to 0.485/ and its width 
equal to 0.5/. However, it is usual and accurate enough 
to make it square upon the drawing. * On screws of the 
same diameter the pitch of a square-threaded screw is usually 
made equal to twice the pitch of one with a V thread ; 
therefore the square thread will have only half the amount 
of material at the bottom of the thread that the V thread 
has to resist the shearing action of the load. As the bearing- 
surfaces of this screw are perpendicular to the axis, and the 
force applied parallel to it, there will be no bursting force 
upon the nut ; and as the reaction is nearly equal to the load 
on the square-threaded screw, there will be less friction than 
there is under the same conditions with a V thread; conse- 
quently the square thread is best adapted for transmitting 
motion when the load has to be moved in opposite directions. 

The Knuckle or Rounded Screw-thread is a modifica- 
tion of the square thread in which the top and bottom of each 
thread are made semicircular, as shown in Fig. 379. This form 
of thread is used for rough work and can be readily thrown 
in and out of gear with a portion of a nut. 

The Buttress Screw-thread is a combination of the V 
and square threads, one side being perpendicular, and the 

♦Klein gives />=.o8-f .09^, d x = .gid— .08. 



236 



MECHANICAL DRAWING. 



other inclined at an angle of 45 ° to the axis of the screw, 
&nd has an amount cut from the top and bottom of each 




Fig. 319. 

thread equal to ■§• of the total depth of the thread, as shown 
in Fig. 320. This form of thread can be used only when the 
pressure is on that side of the thread which is at right angles 
to the axis of the screw. 




Fig. 320. 

Exercise 3. — Draw the sectional outline of the square, 
knuckle, and buttress threads shown in Figs. 319 and 320. 
Pitch 1". Scale twice full size. 

Pipe-threads Previous to the year 1862 no common 

system had been agreed upon for the form or proportions 
of pipe-threads. Since that time, owing to the efforts of 
the late Robert Briggs, C.E., who proposed formulae and 
tables for the dimensions of pipes and pipe-threads, a standard 



ELEMENTARY MACHINE DETAILS. 



2 37 



TABLE 1. 
STANDARD DIMENSIONS OF WROUGHT-IRON WELDED TUBES. 

(Briggs Standard.) 



Diameter of Tube. 




Screwed Ends. 








Thickness 












of 






Nominal 
Inside. 


Actual 
Inside. 


Actual 
Outside. 


Metal. 


Number of 

Threads per 

Inch. 


Length of 
Perfect 
Screw. 


Inches 


Inches. 


Inches. 


Inch. 


No. 


Inches. 


l 


O.270 


O.405 


O.068 


27 


O.19 


i 


O.364 


O.540 


O.088 


18 


O.29 


1 


O.494 


O.675 


O.091 


18 


O.30 


i 


O.623 


O.840 


O.IO9 


14 


0.39 


* 


O.824 


I.050 


0.II3 


14 


O.40 


I 


I.O48 


I-3I5 


O.134 


II* 


0.51 


I* 


I.380 


I.660 


O.140 


II 


0.54 


I* 


1. 6lO 


I.900 


O.I45 


Hi 


0.55 


2 


2.067 


2.375 


O.I54 


II* 


O.58 


2* 


2.468 


2.875 


O.204 


8 


O.89 


3 


3-067 


3.500 


O.217 


8 


0.95 


3* 


3.548 


4.000 


0.226 


8 


I. OO 


4 


4.026 


4- 5oo 


O.237 


8 


I.05 


4* 


4-508 


5.000 


O.246 


8 


I. IO 


5 


5-045 


5.563 


O.259 


8 


I.l6 


6 


6.065 


6.625 


O.280 


8 


I.26 


7 


7-023 


7.625 


O.301 


8 


I.36 


8 


7.982 


8.625 


O.322 


8 


I.46 


9 


9.000 


9-625 


0.344 


8 


i-57 


IO 


10.019 


10.750 


O.366 


8 


1.68 



Taper of conical tube-ends, 1 in 32 to axis of tube (f in. per foot total taper), 

system has been generally used and was formally adopted by 
the manufacturers of wrought-iron pipes and boiler-tubes and 
by the Association of Manufacturers of Brass and Iron Steam-, 
Gas-, and Water-work of the United States. 

The following is an extract from a paper by Mr. Briggs 
as given in the report of the American Society of Engineers: 

11 The thread employed has an angle of 6o° ; it is slightly 
rounded off, both at the top and at the bottom, so that the 
height or depth of the thread, instead of being exactly equal 
to the pitch, is only four fifths of the pitch, or equal to 0.8—, 



2 3 8 



MECHANICAL DRAWING. 






if n be the number of threads per inch. For the length 
of tube-end throughout which the screw-thread continues 
perfect the empirical formula used is T— (o.8Z> + 4.8) X- 
where D is the actual external diameter of the tube through- 
out its parallel length, and is expressed in inches. Further 
back, beyond the perfect threads, come two having the same 
taper at the bottom, but imperfect at the top. The remain- 
ing imperfect portion of the screw-thread, furthest back from 
the extremity of the tube, is not essential in any way to this 
system of joint ; and its imperfection is simply incidental to 
the process of cutting the thread at a single operation. 

Exercise 4. — Draw a section of a pipe-screw (Fig. 321) for 
a wrought-iron pipe 8" in diameter. Scale five times full size. 




L ^ THffEADS _Ji_2THflrAPS± Comblftf Thbitao 

V^^/MP£RrECT ^FUUA.TRO<$ LOHPLCTC IHBCAO 

U 4p *L — ip — X T — 



Fig. 321. 

Construction. — Draw two lines parallel to each other at 
a distance apart equal to the thickness of metal as given in 
the table ; then draw the vertical line 2 to represent the end 
of the pipe, and from 2 along the line I mark off 3, 4, equal 
to T. Taper 1 in 32 means an inclination of 1 unit in height 
to every j 2 units in length. From the point 4 draw the line 5 
at the required inclination. On the line 5 from where it 
intersects 2 mark off points at a distance apart equal to the 
pitch, and through these points with the 30 triangle draw the 



ELEMENTARY MACHINE DETAILS. 



2 39 



threads. The bottoms of the last 4 threads are cut off by 
drawing a line from the bottom of the last thread that is 
full at the bottom to a point on the surface of the pipe which 
is a distance beyond the screwed part equal to the pitch. 

Screw-thread Conventions. — The method of drawing 
screws to represent their true form is shown in Fig. 315, 
but it is quite obvious that it is unnecessary for the drafts- 
man to perform this lengthy geometrical construction to 
indicate each screwed piece upon the drawing. Instead 
he adopts some convention suitable to the class of draw- 
ing he is making that can be quickly drawn and is generally 
understood to represent a screw-thread. Fig. 322, No. I, 





T 



shows a convention for a double V thread; No. 2, a single 
V thread; No. 3, a single square thread; No. 4, a single 
left-hand V thread; No. 5, a double right-hand square 
thread; No. 6, any V thread of small diameter; No. 7, 
any thread of very small diameter. The method adopted 
on rough drawings and sketches is shown at No. 7. The 
dotted lines indicate the bottom of the thread, and the 
distance they extend along the piece the length of the 



240 



MECHANICAL DRAWING. 



screwed part. At Nos. I, 2, 4 are shown conventions 
adopted upon finished drawings to represent threaded screws 
of a large diameter and wide pitch. There are various ways 
of improving the appearance of this convention : one is 
by shading the lower lines of each thread, as shown in Fig. 
324; and another method is to fill in completely the 
under side of the thread. At No. 6 is shown a method 
adopted on working drawings to represent screw-threads 
upon pieces of a small diameter or large screws drawn 
to a small scale. Here the narrow lines indicate the 
top and the wide lines the bottom of the screw-thread. 
When a very long screw has to be represented upon a draw- 
ing, as is often the case with the square-threaded screw, a 
few threads are drawn at the beginning of the screwed part, 
and the length of the screw is indicated by dotted lines drawn 
from the bottoms of the threads. 

The Nut. — The most common application of the screw 
for producing contact pressure is the bolt, used in conjunction 
with a nut, of which there are different forms. The form 
most in use is the hexagonal (Fig. 324). 

The standard proportions for hexagonal nuts are : 

H= height = diameter of bolt (d). 

F = distance across the flats = i\d -\- \ of an inch. 

D = distance across the corners = (\\d-\- -J-") 1.155. 

Fig. 323 shows the true form of the curves when the end 
of the nut is machined to form a part of a sphere or cone. 
This rounding or bevelling off of the corners is called cham- 
fering. The radius r of the chamfering is made from i^d to 
2dy and the angle a is made from 6o° to 45 ° with the axis of 
the nut. When representing nuts upon a drawing they should 



ELEMENTARY MACHINE DETAILS. 



241 



always be drawn to show the distance across the angles, as in the 
elevation Fig. 323. 

Exercise 5. — Draw the true curves of a hexagonal nut for 
a bolt 6" in diameter when the top of the nut is chamfered 




Fig. 323. 
off to form a part of a sphere with a radius r = I J times the 
diameter of the bolt (d), and when the chamfering is a part 



242 MECHANICAL DRAWING. 

of a cone the side of which makes an angle of 45 with the 
axis of the nut, as shown in Fig. 323. 

Construction. — Begin with the plan, first locating the cen- 
tre c, and with f as a centre and a radius equal to \d draw 
the quadrant representing the hole in the nut, and from the 
same centre and a radius equal to half the distance across the 
flats F draw the quadrant Q, and on this quadrant circum- 
scribe a part of a hexagon with the 30 triangle and T square, 
as shown in Fig. 324. Draw the part elevations and end 
views, and with r as a radius and the centre on the centre 
line draw the arc 5, which represents the spherical chamfer, 
and on the lower elevation draw the angle a. Divide eb into 
any number of divisions, say 6, at points 1, 2, 3, 4, $d. 
Where perpendicular lines drawn through these points intersect 
the arc 5 and line L draw the horizontal lines 7, 8, 9, 10, 11, 
12, 13, and with c as a centre and radii ci, c2, c$, C4, c$ 
draw arcs, and from where these arcs intersect the inclined 
face of the nut draw vertical lines to intersect the lines 7, 8, 
9, 10, etc. These points of intersection will be points of the 
curve on the side face of the nut. The curve of the front 
face will be an arc of a circle. To find the curves on the side 
view draw a line 15 say \" below and parallel to the lower 
face of the nut in plan, and a perpendicular line 14 half 
an inch to the left of the end view; where the arcs drawn 
through the points 1, 2, 3, etc., from the centre c cut the 
inclined face of the nut in plan draw horizontal lines to inter- 
sect the line 14 ; and with a centre at the intersection of the 
lines 14 and 15 revolve the lines 17, 18, 19, 20, 21, 22, 23 
on to the line 15 and draw perpendicular lines through the 
points of intersection. The line 17 revolved will be the cert- 



ELEMENTARY MACHINE DETAILS. 



43 



tre of the nut face on the end view, and the intersection of 
the lines 17, 18, 19, 20, 2 1, 22, 23 with the horizontal lines 
7, 8, 9, 10, 11, 12, 13 will be points on one half of the re- 
quired curve. To complete the curve, with a centre at the 
intersection of the line 17 and the top of the nut mark with 
the compasses corresponding points on the other side of the 
line 17. 




Fig. 324. 

A Conventional Method of representing large nuts on 
drawings is shown in Fig. 324. In this representation the 
curves of the nut are arcs of circles and the corners are 
chamfered off at an angle of 45 ° to the axis of the nut, 



244 



MECHANICAL DRAWING. 

TABLE 

UNITED STATES STANDARD OF 



Screw-threads. 



Diameter 

of 

Screw. 


Number 

of 
Threads 
per Inch. 


Diameter 

at 

Bottom 

of 

Threads. 


\rea at 

Bottom 

of 

Threads in 

Square Inches. 


Area of 

Bolt Body 

in 

Square Inches. 


% 
5/16 

H 

7/16 

% 
9/16 

% 

% 


20 
18 
16 
14 
13 
12 
II 
10 

9 


.185 
.240 
.294 

•344 
.400 

•454 
.507 
.620 

•73i 


.027 

•045 
.068 

•093 
.126 
.162 
.202 
.302 
.420 


.049 
.077 
.IIO 
.150 
.196 
-249 
•307 
•442 
.601 


1 

M 


8 

7 

7 

6 

6 

1% 

5 

3 


.837 
.940 
1.065 
1. 160 
1.284 
1.389 
1. 491 
1. 616 


•550 

•694 

.893 

I.057 

1.295 
I. 515 
I.746 
2.051 


.785 
•994 
1.227 
1.485 
1.767 
2.074 
2.405 
2.761 


2 
2% 

2% 


4K 
4K 
4 
4 


1. 712 
1.962 
2.176 
2.426 


2.302 
3.023 

3-719 
4.620 


3.142 
3.976 
4.909 
5 -940 




3X 

3X 
3 


2.629 
2.879 
3.100 

3-317 


5-428 
6.510 
7.548 
8.641 


7.069 

8.296 

9.621 

11.045 




3 

2^ 
2# 


3-567 
3.798 
4.028 
4.256 


9-963 
II.329 
12-753 
14.226 


12.566 
14.186 
15.904 
17.721 


6 


2^ 
2^ 
2^ 
2^8 
2X 


4.480 
4.730 
4-953 
5-203 

5.423 


I5.763 
17.572 
19.267 
21.262 
23.098 


I9-635 
21.648 
23.758 
25.967 
28.274 



Note.— The above table gives the sizes of the rough nuts and bolt-heads. The finished 



ELEMENTARY MACHINE DETAILS. 



245 



SCREW-THREADS, BOLTS, AND NUTS. 



Nuts. 


Heads. 


Tap Drill. 






L/ 




h"^ — 1 


M, \ 




|>U 










h 


"i 












-_ 




1 




yw/s/s. 




(Xil) 


to; 




3 








CZJ 




O 


X 


x 


37/64 


7/10 


X 


X 


3/l6 


5/16 


19/32 


11/16 


10/12 


5/16 


19/64 


X 


H 


u/16 


51/64 


63/64 


H 


n/32 


5/16 


7/16 


25/32 


9/10 


u\ 


7/16 


25/64 


23/64 


.X 


# 


1 


iH 


X 


7/16 


13/32 


9/16 


31/32 


*H 


ill 


9/16 


31/64 


15/32 


# 


iA 


T 7 

1*5 


i# 


3 


17/32 


17/32 


X 


iX 


'If 


T 49 


^ 


H 


H 


# 


T 7 

r T5 


Ifi 


2^V 


# 


23/32 


X 


I 


I# 


lj& 


»H 


1 


13/16 


27/32 


*H 


III 


*& 


*A 


iX 


29/32 


31/32 


iX 


2 


»A 


2|f 


iX 


1 


T 3 

X 1TS 


I# 


3 

2 lff 


2H 


3/* 


irt 


T 8 
T 37 


*A 


IX 


2^ 


2^ 


3ll 


iX 


*A 


4 


I* 


2A 


/,31 


3X 


i# 


T 9 
I 37 


m 


iX 


2X 


3tV 


3ff 


iX 


I# 


i]4 


o 1 5 


3*1 


4& 


if 


i*l 


i# 


2 


3X 3^ 


4H 


2 


iy 9 w 


iX 


2X 


3X 


4tV 


4li 


2X 


iX 


1 F? 


2/2 


3X 


4# 


5fi 


2^ 


ill 


*ft 


2% 


4X 


4|f 


6 


2 X 


2^ 


2 T V 


3 


4^ 


5^ 


6U 


3 , 


2A 


2^ 


3X 


5 


5y| 


7tV 


3X 


2/2 


«8I 

z 32~ 


3K 


5H 


6& 


71! 


3X 


2H 


3A 


3X 


5X 


6fi 


8^ 


3X 


2^ 


3M 


4 


6^ 


7A 


8ft 


4 


3tV 


335 


4X 


6X 


7t\ 


9A 


4X 


3X 


3 T f 


4X 


6^ 


7fi 


9U 


4% 


3tV 


4A 


4X 


1% 


CI 3 
°S2 


10X 


4X 


3^ 


4A 


5 


iH 


027 


lot! 


5 


3H 


4X 


5X 


8 


9a* 


TT 2S 


5X 


4 


4X 


5X 


8^ 


9ff 


11^ 


sX 


4fV 


4fi 


5X 


8X 


10A 


I2# 


sX 


4 3 A 


5A 


6 


9X 


«>H 


,,16 

I2 rs 


6 


4A 


5A 



H=d-x/xV'\ F= iid + 1/16": A=4-i/i6"; A, = 



ri^+i/16' 



246 



MECHA NIC A L DRA WING. 



The A. L. A. M. Standard Screws and Nuts.— The 

form of the screw thread is the U. S. Standard as shown in 
Fig. 316. The number of threads per inch for the A. L. A. M. 
bolts and nuts is given in Table 3. Bolts and nuts are 
made of steel, whose tensile strength must not be less than 
100,000 pounds per square inch and elastic limit not less 
than 60,000 pounds per square inch. 



TABLE 3. 

A. L. A. M. STANDARD SCREWS AND NUTS. 



d 


Number of 
Threads. 


F 


G 


H 


k 


M 


i 


\ 


28 


1 


ft 


ft 


ft 


ft 


ft 


ft 


24 


* 


A 


a 


ft 


ft 


ft 


t 


24 


ft 


I 


M 


i 


i 


ft 


7 


20 


tt 


i 


f 


i 


i 


ft 


h 


20 


a 

4 


* 


ft 


ft 


ft 


ft 


ft 


18 


I 


A 


39 

64 


ft 


ft 


* 


t 


18 


15 

16 


ft 


If 


i 


1 


i 


tt 


16 


I 


ft 


if 


1 


1 


* 


I 


16 


I* 


ft 


H 


i 


1 


i 


I 


14 


ii 


ft 


ft 


i 


1 


* 


I 


14 


ift 


ft 


1 


i 


1 


i 



The length of the threaded portion of the bolt should be about 
1 \ times the diameter. 

Bolt heads and plain nuts are flat chamfered, as in Fig. 

3 2 4. 

Castle nuts have a spherical chamfer, as in Fig. 324. 

Bolts and nuts are finished with what is known as screw 
makers' " semi-finish." 

Screws, screw heads, and plain nuts are left soft, while castle 
nuts are case-hardened. 



ELEMENTARY MACHINE DETAILS. 



2 4! 



The body diameter of the screw is one-thousandth of an inch 
(.001) less than the nominal diameter. The clearance between 
top and bottom of threads in nuts is correct when the top 
is made from two-thousandths to three-thousandths of an 
inch large. 

Nuts are made to fit without apparent shake. Fig. 325 shows 
the A. L. A. M. bolt and castle nut. The facing under the head 



{ 1 * 

$.b ~W*( 

[ 1 jL 




and nut is made equal in diameter to the distance across the 
flats and is made so that the scratching of the nut when it is being 
screwed on to a finished surface will not show. It also increases 
the pressure per square inch. 

Split Pins, when made of a uniform diameter from wire 
of a semicircular cross-section and provided with a head, 
as in Fig. 326, are used for preventing pieces from sepa- 
rating, while allowing a slight motion in the direction of 
the axis of the piece that they pass through. The method 
of drawing split pins is clearly shown in Fig. 326. The diam- 
eter of the pin, in proportion to the diameter d of the piece 
it passes through, may be = .05^ + .13, taking the nearest 
size in jfe". 



2 4 8 



MECHANICAL DRAWING. 



Taper Pins, shown in Fig. 327, are used for securing one 
piece to another in a fixed position. They are sometimes 




Fig. 326. 

split at the small end, and opened out in the same manner 
as the ordinary split pin, to prevent slacking back. The 
diameter of the tapered pin at the large end, in proportion 




Fig. 327. 



to the diameter (d) of the piece through which it passes, may 
be made = .o6d + .13 and taking the nearest size from Table 4 
(page 249). 

Keys are employed to connect wheels, cranks, cams, 
etc., to shafting transmitting motion by rotation. They are 
generally made of wrought iron or steel, and are commonly 



ELEMENTARY MACHINE DETAILS. 



249 



TABLE 4. 

STANDARD STEEL TAPER-PINS. 

Taper one-quarter inch to the foot. 



dumber 


O 


I 


2 


3 


4 


5 


6 


7 


8 


9 


10 


Diameter at { 
larye end | 


.i* 


.17. 


•193 


.219 


.250 


.2S9 


•34i 


.409'. 492 


•59i 


.706 


Approximate ) 

fractional V 

sizes ) 


5/32 


II/64 


3/16 


7/32 


X 


19/64 


11/32 


13/32 


^ 


19/32 


23/32 


Longest limit \_ 
of length ) 


I 


iX 


l/z 


iU 


2 


2X 


3X 


3% 


4^ 


sX 


6 



rectangular, square, or round in cross-section. The form of 
key in general use is made slightly tapered and fits accurately 
into the key-way, offering a frictional holding power against 
the keyed piece moving along the shaft. The groove or part 
where the key fits on the shaft, and the groove into which it 
fits on the piece it is holding is called the key-bed, key- 
way or key-seat. For square or rectangular keys, when the 
keyed piece is stationary on the shaft, the bottom of the 
groove on the shaft is parallel to the axis, while that of the 
groove in the piece it is securing is deeper at the one end 
than the other to accommodate the taper of the key. 

Keys may be divided into three classes: 1. Concave or 
saddle key; 2. flat key; 3. sunk key. 

Saddle Key. — This form of key has parallel sides, but is 
slightly tapered in thickness and is concaved on the under 
side to suit the shaft, as shown in Fig. 328. As the holding 
power depends entirely upon the frictional resistance, due to 
the pressure of the key on the shaft, the saddle key is only 



250 



MECHANICAL DRAWING. 



adapted for securing pieces subjected to a light strain. When 
this key is used for securing a piece permanently, the taper is 
usually made 1 in 96, but when employed on a piece requir- 
ing to be adjusted, such as an eccentric, the taper is increased 
to I in 64 to allow the key to be more easily loosened. 




Fig. 328. 



3 2 9 



Flat Key. — This form of key, Fig. 329, differs from the 
saddle key in that it rests on a flat surface filed upon the 
shaft. It makes a fairly efficient fastening, but as it drives 
by resisting the turning of the shaft under it, there is a tend- 
ency to burst the keyed-on piece. 



TABLE 5. 

DIMENSIONS OF SADDLE AND FLAT KEYS. 



D 


1 


iU 


iy 2 


iU 


2 


2^ 


3 


3M 


4 


5 


6 


7 


B 


% 


5/16 


3 /8 


7/16 


% 


H 


U 


H 


1 


iH 


tH 


iH 


T 


3/16 


3/16 


3/16 


% 


% 


5/16 


5/16 


n 


H 


7/16 


y* 


9/16 



I* 



Sunk Keys are so called because they are sunk into the 
shaft and the keyed-on piece, Fig. 330, which entirely pre- 
vents slipping. For engine construction they are usually 
rectangular in cross-section and made to fit the key-seat on 
all sides. When subjected to strains suddenly applied, and 



ELEMENTARY MACHINE DETAILS. 



251 




Fig. 331. 

in one direction, they are placed to drive as a strutj 
diagonally, as in Fig. 331. 




Fig. 330. 



Fig. 332. 



The following table, taken from Richards's " Machine 
Construction," agrees approximately with average practice: 

TABLE 6. 

DIMENSIONS OF RECTANGULAR SUNK KEYS. 



D 


1 


1% 


1% 


iU 


2 


2^ 


3 3'A 


4 


5 


6 


7 


8 


B 


% 


5/16 


H 


7/16 


% 


S /8 


% % 


1 


1/8 


ifg 


iH 


*x 


T 5/32 


3/16 


% 


9/32 


5/16 


tt 


7/16 % 


H 


n/16 


13/16 


n 


I 



In mill-work, for fastening pulleys, gear-wheels, coup- 
lings, etc., to shafting they are made slightly greater in depth 



252 



MECHANICAL DRAWING. 



than breadth. For machine tools they are generally square 

in cross-section. The following table gives the sizes of keys 

used by Wm. Sellers & Co. both for shafting and machine 

tools: 

TABLE 7. 



3^ 
11/16 





a 


a 


„ 


a 


„ 


a 


a 


a 


D 


i# 


^ 


2 


2^ 


*A 


*U 


3 


3X 


B 


5/i6 


5/16 


7/16 


7 /i6 


9/16 


11/16 


n/16 


11/16 


T 


% 


H 


A 


A 


h 


% 


% 


X 





n 


u 


„ 


n 


a 


a 


lf 


a 


II 


D 
B 
T 


4 

13/16 


aA 
13/16 

ft 


5 
13/16 

7 A 


s l A 

15/16 

1 


6 

15/16 

1 


I5/I6 

1 


7 
1^ 


VA 
1^ 


8 
1^ 



Round Keys. — Taper-pins (Fig. 332) are sometimes used 
as keys to prevent rotation where a crank or wheel is shrunk 
on to the end of a shaft or axle. Round keys are used in 
such a case because of the ease in forming the key-way, 
which is simply a tapered round hole drilled half into the 
shaft and half into the shrunk-on piece. The standard pro- 
portions of the pins are given on page 249. The size at the 
large end nearest to £ of the shaft diameter may be used for 
this purpose. 

Fixed Keys are used when it is undesirable to cut a long 
key-way on the shaft to allow the key to be driven into place 
after the keyed-on piece is in position. The fixed key is 
sunk into the shaft, as in Fig. 333, and the keyed-on piece is 
driven into position after the key is in place. 

When a keyed-on piece has to be adjusted to different 
positions on the shaft, to avoid the trouble of drawing a 
tight key in and out, it is made to slide in the key-way, and 
the keyed-on piece is held against moving along the shaft by 
means of set-screws, as shown in Fig. 334- 



ELEMENTARY MACHINE DETAILS. 



253 




Fig. 333. Fig. 334. 

Sliding Feather Key. — This system of keying secures 
the piece to the shaft, to transmit motion of rotation, and at 
the same time allows the keyed-on piece to move along the 




Fig. 335. Fig. 336. 

shaft. They may be secured to the keyed piece and slide in 
a groove on the shaft, as in Fig. 335, or secured to the shaft 
and slide in the groove in the keyed piece, as in Fig. 333. 
The dimensions for this form of key may be taken from 
Table 7. 

Woodruff Keys.— This system of keying (Fig. 337) is 
used for machine tools, or wherever accurate work is of first 
importance. With this form of key, as the key rights itself 
to the groove in the keyed-on piece, there is no danger of 



254 



MECHANICAL DRAWING. 



the work being thrown out of true by badly fitted keys, and, 
being deep in the shaft, it cannot turn in the key seat 




No. 


A 


B 


c 


D 


6 


ft 


A" 


A" 


1 n 


8 


1 


A' 


5 // 
64 


A" 


IO 


in 

8 


A' 


A" 


A" 


ii 


r 


A" 


A" 


4" 


13 


i" 


A" 


A'- 


A" 


i7 


it" 


A" 


7 /.' 
64 


A" 


20 


ir 


A" 


A" 


A" 



Tor if" 

i" or if" 

*" or if" 

i" 

i|" 

ii" or i&' 

if" or i A' 



No. 


/I 


5 


c 


D 


d 


21 


ii" 


\" 


r 


5 

64 


iy toif" 


22 


If" 


1 ■•/ 

4 


i" 


A 


lA'toif 


23 


I*" 


A" 


A" 


A" 


itt"toir 


24 


I*" 


\" 


i" 

8 


7 // 

64 


itt" to if" 


2S 


I*" 


A" 


A" 


7 /• 
64 


lif" tO 2\" 


26 


2*" 


A" 


A" 


w 


2" to 2f" 


G 


Ii' 


r 


3 /' 

16 


7 // 
64 


2" tO 2\" 



&\- 




Fig. 338. 



The "Woodruff " key, reaching deeper into the shaft than one 
of ordinary construction, is more firmly imbedded, and hence 
capable of standing a much greater strain. 

It is impossible for a Woodruff key to roll over in its seat, as is 



ELEMENTARY MACHINE DETAILS. 



2 55 



often the case with an ordinary key. In case of an accident, 
Woodruff keys have been known to shear off without damaging 
pulley or shaft, where an ordinary key of the same width would 
roll in the seat and destroy both pulley and shaft. Whitney 
Manufacturing Company. 



COTTERS 

are keys employed to connect pieces which are subjected to 
tensile and compressive forces. They are driven transversely 




Fig. 339. 

through one or both of the connected pieces and transmit power 
by a resistance to shearing at two cross-sections. The cotters 
are usually made rectangular in cross-section, and the ends 
rounded, as shown in Fig. 339. 



256 MECHANICAL DRAWING. 

The cotter-way with the rounding ends is generally 
adopted, as it is easier to make, which is done by drilling two 
holes of a diameter equal to the thickness of the cotter and 
cutting out the metal between them. Again, this form of 
cotter-way does not weaken the cottered pieces to quite the 
same extent as when the corners are left sharp. The cotters, 
however, are not so easily fitted into cotter-ways with round 
ends, and for that reason some engineers make the cotters of 
rectangular cross-section, fitted into corresponding cotter^ 
ways. 

Taper of Cotters. — When cotters are employed as a 
means of adjusting the length of the connected pieces, or for 
drawing them together, they are made tapered in width, as in 
Fig. 339, but when used as a holding-piece only, the side? are 
parallel. When tapered cotters depend upon the friction 
between their bearing-surfaces for retaining them in position 
the taper should not be more than 1 in 24 (J" per foot), but 
where special means are employed for holding the cotter 
against slacking, the taper may be made as great as 1 in 6 
(2" per foot). 

Forms and Proportions of Cotter-joints. — When the 
fastening is subjected to tension only, the arrangement shown 
in Fig. 339 is used for securing two pieces together by means 
of a cotter. Fig. 339 shows a method of fastening two 
rods, R and R\ together to resist thrust and tension. The 
joint is made by fitting the end of the rod R into a socket 5 
formed on the end of the rod R ' ', and through the socket and 
rod end driving a cotter until the collar C bears against the 
socket end. \ 






ELEMENTARY MACHINE DETAILS. 257 

As a cotter-joint is proportioned to withstand the greatest 
longitudinal force transmitted by the rod, all parts will there- 
fore be proportional to the diameter d x of the rod, unless 
where the dimensions of the rod are increased to insure stiff- 
ness. The following proportions are in accordance with good 
practice: 

b, breadth of cotter = 1.3^; 

/, thickness of cotter = .3^,; 

d> diameter of pierced rod = \.2d x \ 

D, diameter of socket in front of cotter == 2.4^ or 2d. 

D x , diameter of socket behind cotter = 2d x \ 

D ti diameter of collar on rod R = 1.5^,; 

/, thickness of collar on rod R — \d x ; 

/, the length of the rod and socket beyond the cotter = from 

\d x to d x . 

VVhen d is known the diameter of the solid rod (d\) = .82^. 
The clearance c may be made \". The cotter need not extend 
beyond the greatest diameter of the socket more than \" when 
driven home. 

COTTER AND GIB. 

When one of the pieces connected by the cotter is 
a thin strap, as in Fig. 340, a second cotter, called a 
gib, is used. The gib is provided with a head at the 
ends which project over the strap S, thus preventing it 
(the strap) from being forced open by the friction between it 



2S< 



MECHANICAL DRAWING. 



and the cotter as the latter is driven into place. Figs. 340 
and 341 show the application of gib and cotter to strap-end 
connecting-rods, where R is the rod and S the strap. When 
two gibs are used, as . in Fig. 342, the sliding surface on each 
side of the cotter is the same. Instead of having both gibs 
tapered, as shown in Fig. 342, one of them may be parallel 
and the taper all on one side of the cotter. The strength of 
the gib and cotter in combination is made the same as the 




Fig. 34c. 



Fig. 341. 



Fig. 342. 



single cotter and should be proportional to the strap 5. The 
working strength of the strap at the thinnest part is found by 
the equation 



2BTf t = P. 



from which 



T = 



2Bf t 



(12) 



where Pis the maximum pull on the xo\ T the thickness, 



ELEMENTARY MACHINE DETAILS. 



2 59 



and B the breadth of the strap. Then as the gib and cotter 
are to have the same strength as the single cotter, and as B is 
equal to, or a little greater than d (the diameter of the rod), t 
may be made equal to .25$ and 



I 2BT 
V.7854 



T', the thickness of the strap where it is pierced by the cotter, 
should not be less than 1.3 7\ V, the distance from the gib to 
the end of the strap, = 2 J 1 . /, the distance from the cotter to 
the end of the rod, = 1.5^ c, the clearance, should not be less 
than c f (the difference between the widest part of the eotter and 
the width of the cotter at the top of the gib-head). The method 
of constructing gib-heads is shown in Fig. 341, where h, the height 
of the gib-head, = 1 \t. 

Nut Wrench. — Fig. 343 shows a common straight nut 




wrench. They are made of wrought iron or steel, drop forged. 
Table 9 gives the usual proportions. 



260 



MECHANICAL DRAWING. 



TABLE 9. 

PROPORTIONS FOR WRENCHES. 



B = WX.& 



D = WX.6$ 

F=WX.2S 



L = WX.7 




Fig. 344. 

Helical Springs. — The following formulae is given by 
Clarke, who quotes from a report on safety valves made by 
the Inst, of Engrs. and Shipbuilders of Scotland: 

d 3 Xw Iwd 

E = KTt:^ D = x — , for round steel. 



and 



D = ^l — , for square steel. 
4-9 



E = compression or extension of one coil in inches; 

d= diameter from center to center of steel bar of which the 

spring is made, in inches; 
w = weight applied in pounds; 

D = diameter, or side of the square of the steel bar, in six- 
teenths of an inch; 
C=a constant, which may be taken as 22 for round steel 
and 30 for square steel. 

To obtain the total deflection for a given spring, multiply the 
deflection for one coil by the number of free coils. 



ELEMENTARY MACHINE DETAILS. 



261 



In Fig. 344, 4 is an example of a helical tension spring and 5 
that of a compression spring. 




Fig. 345. 

Fig. 345 shows an example of a coil spring for a steam safety- 
valve with its spindle. 

Cast-iron Flanges. — Figs. 346 and 347 show drawings of 
cast iron flanges of ordinary design. Their correct proportions 
are given in Table 10. 




Fig. 346. 



Fig. 347. 



Chains. — Fig. 348 shows a drawing of a common end link 
and narrow shackle used for general purposes. Table 11 gives 
the United States Navy standard proportions. 



262 



MECHANICAL DRAWING. 



TABLE 10. 

PROPORTIONS FOR FLANGES. 



Dia. 














Dia. 












of 


A 


5 


C 


Z? 


E 


F 


of 


A 


B 


C 


D 


E 


Bolt. 














Bolt. 












,, 


// 


// 


// 


// 


n 


tr 


// 


/> 


n 


n 


t, 


n 


4 


6 


it 


1 


1% 


4 


t 


1 


if 


8 


h 


1 


A 


1 


7 


1* 


if 


T* 


t 


1 


4 


3i 


Ii 


\ 


TV 


A 


1 


8 


2* 


if 


If 


* 


I 


1 
4 


4* 


if 


1 


1 


tV 


ii 


10 


2| 


2* 


I* 


3 

4 


I* 


1 


6* 


2i 


Ii 


1 


4 


2 


12 


4 


3i 


^ 


7 
8 


It 


if 


9 


3 


14 


ll 


tk 


2i 


15 


5 


4 


2 8 


I 


2* 


it 


IOj 


34 


if 


1* 


f 


3 


18 


6 


4* 


3* 


I* 


2f 


2 


1.3 


4t 


: 8 


if 


1 




Fig. 348. 



TABLE 11. 



A 


Ai 


5 


C 
6* 


4* 


E 

n 

i4 


F 
2^ 


t 


H 

3 


7 

2f 


1 
4 


L 
4i 


M 


N 
5 

8 





n 
I 


I* 




3l 


l| 


I4 


4* 


74 


S* 


if 


^ 


T^ 


3i 


3i 


5 

T6 


54 


6 


f 


44 


it 


if 


4A 


8* 


Sf 


it 


2lV 


A 


3* 


34 


& 


6 


■6* 


1 


4f 


I* 


if 


Si 


0* 


6* 


2i 


3t 1 6 


A 


44 


4 


t 


7 


7f 


i 


54 


if 


I* 


6t 


nf 


8 


2f 


3+* 


tt 


54 


5 


Vo 


8 


9i 


I 


6f 


ii 


2 


6H 


nf 


8* 


2f 


3tt 


tt 


5* 


5 


7 
T6 


84 


9t 


ii 


6* 



ELEMENTARY MACHINE DETAILS. 



263 



Ball Crank Handle. — Fig. 349 shows a drawing of a form 
of handle used for ball cranks on machine tools. The dimensions 
are given below in Table 12. 




HGK-£3 



Fig. 349. 



o 1 



-C7 



*pZZZ23ZBL 



Fig. 350. 



W/M///A 



TABLE 12. 



No. 


A 


B 


<T 


D 


£ 


F 


£ 





2i 


\ 


A 


H 


tt 


I 


A 


1 


2| 


5 

f 


J 


E 


£ 


1 


f 


2 


3i 


1 


i 


1 


ft 


f 


1 


3 


3* 


1 
4 


_5_ 

32 


n 3 * 


tt 


i 


ft 


4 


4 


1 


A 


i* 


A 


§i 


A 


5 


4i 


J 


h 


1 A 


M 


if 


U 



Washers. — Fig. 350 is a cross-section of the ordinary circular 
washer for all kinds of bolts. Table 13 gives the proportions 
for different diameters of bolts. 



TABLE 13. 



Diam. of 


j 


D 


u. s. 


Diam. of 


d 


z? 


U. S. 


Bolt. 


Wire Gauge 


Bolt. 


Wire Gauge 


ft 


\ 


A 


No. 18 


1 


It 


4 


No. 9 


\ 


A 


1 


No. 16 


I 


1* 


2\ 


No. 9 


ft 


1 


1 


No. 16 


ii 


ii 


2f 


No. 9 


i 


A 


1 


No. 14 


ii 


if 


3 


No. 9 


ft 


1 


li 


No. 14 


if 


^i 


3i 


No. 8 


§ 


A 


if 


No. 12 


1* 


if 


3* 


No. 8 


A 


1 


ii 


No. 12 


if 


if 


3l 


No. 8 


1 


tt 


if 


No. 10 


ii 


ii 


4 


No. 8 


i 


H 


2 


No. 10 


2 


4 


4* 


No. 8 



264 



MECHANICAL DRAWING. 




"\ 



r 



w 



Fig. 351. 



CRANE HOOKS. 

Notation: * 

P = load in pounds; 
A = area in square inches; 
R 2 = square of the radius of gyration; 
/= allowable fiber strain in pounds per square inch. 

P Pxe x _P Pxei 
J~~A ~T~~ A AR 2 ' 



A 



1 + 



xe\ 
R 2 



. . . (General Formula) 



* American Machinist, Oct. 31, 1901. 



ELEMENTARY MACHINE DETAILS. 

For section considered as a trapezoid 

A J-±^ Xd , . . (I) R2 _dW + 4 bc + c>) 



b + 2C d 



(3) 



X = 



b + 2c d\ 



Assuming b =.656^; c = .2id. Then 
P d 3 



f 7. 79^+11. n^r' 
D = 2r+i%d, di = o.$d. 



26; 

(2) 
(4) 

(5) 




Fl c 35- 



P and / being known, assume r to suit. Divide P by / and 
.find the quotient in the column headed by the required r, in 



2 66 



MECHANICAL DRAWING. 



Table 14. At the side of the table in the same row will be found 
the necessary depth of section d. 



TABLE 14. 





r 


d 


.50 


.75 


1 .00 


1. 25 


1 -SO 


1. 75 


2 .00 


2.25 


2 .50 


2.75 


3 .00 


2.00 


.378 


•335 


.300 


.271 


.248 


.228 


.212 


.197 


.184 


•173 


.164 


2.25 


-493 


.440 


•397 


.362 


•333 


.308 


.286 


.267 


.251 


.237 


.224 


2.50 


.624 


.562 


.511 


.468 


• A3 2 


.401 


•375 


-352 


-330 


.312 


.296 


2.75 


.771 


.698 


-639 


.589 


• 54^ 


•509 


-477 


-448 


.423 


.400 


.380 


3.00 


•934 


.851 


-7«3 


.725 


-675 


.631 


-592 


-558 


.528 


-501 


-477 


3.25 


1. 112 


1. 019 


.941 


-875 


.818 


.767 


.722 


.682 


.646 


.614 


-585 


3-50 


1.306 


1.204 


1. 117 


1.042 


-975 


.918 


.867 


.82c 


-778 


• 742 


.707 


3.75 


I-SI7 


1.404 


1.307 


1.223 


1. 140 


[.084 


1.025 


-973 


.926 


.882 


.843 


4.00 


1-743 


1.620 


i-5!4 


1. 421 


i-338 


1 .265 


1. 199 


1. 139 


1.086 


i-°37 


-993 



In Table 15 the proper proportions for the given loads have 
been worked out. 

TABLE 15. 



Tons 


Lbs. 


r 


d 


D 


b 


C 


di 


i 





N 


5 


T 


W 


f 


* 


TOOO 


1 


2 


5 


itk 


h 


1 


ii 


1 


4 


5 


if 


1 


i* 


1 


2000 


1 


2i 


5& 


iM 


h 


ii 


if 


it 


^ 


7 


2f 


ifk 


ii 


2 


4000 


it 


3 


7 


2 


5 

8 


2 


2 


14 


Ii 


9 


3* 


if 


2 


A 


5000 


ii 


3* 


8i 


2k 


3 
4 


-4 


*k 


2 


4 


10 


4 


2 


2* 


5 


I OOOO 


2h 


5i 


12* 


3 


1^ 


2* 


3 


2h 


Ii 


14 


6 


2f 


4f 


10 


20000 


4 


Ih 


19* 


5 


iM 


4 


4l 


4 


2 


15 


7 


3* 


6 



Hand Wheel. — Fig. 353 shows a drawing of a standard hand 
wheel used for globe valves, etc., and in Table 16 is given the 
usual proportions. 



ELEMENTARY MACHINE DETAILS. 



267 









TABLE 16. 








Dia. 


A 


B 


b 


d- 


7 


* 


L 


4 


i 


i 


A 




4 


7 

32 


i 


5 


& 


& 


A 


1* 


A 


7 

32 


it 


6 


I 


1 


1 


T I 

1 4 


A 


J 


if 


7 


& 


H 


16 


if 


ft 


A 


1 


8 


I 


i 


I 


il 


1 


A 


i* 


9 


if 


if 


1* 


if 


if 


ft 


ii 


10 


1 


7 

8 


f 


if 


T6 


1 


i* 


11 


4^ 

16 


if 


a 


T 7 
is 


tt 


! 


If 1 


12 


I 


I 


13 

16 


2 


J 


ti 


1* \ 




Fig. 353. 



Fig. 354- 



Shaft Collars. — Fig. 354 shows a usual design for shaft 
collars made in cast iron. Table 17 gives the correct proportions. 











TABLE 


17. 








Bore. 


B 


Z3 


H 


L 


M 


5 


T 


w 


*A 


if 


2! 


I 


tt 


A 


f 


1 
4 


§ 


Itt 


if 


3i 


1 


if 


i 


i 


A 


f 


2^ 


2* 


4 


ii 


ft 


A 


f 


1 


if 


2H 


2i 


4l 


i* 


ft 


1 


2 

4 


7 
to 


1* 


3A 


2| 


5f 


1* 


1 


§ 


a 

4 


_7_ 
16 


ii 


3H 


3 


6| 


if 


iA 


A 


1 


1 


iA 


4A 


3i 


7f 


2 


rA 


1 


1 


A 


ii 


4« 


3f 


8! 


2* 


il 


A 


ii 


A 


if 


5A 


3t 


9i 


2* 


1* 


A 


ii 


A 


if 



2 68 MECHANICAL DRAWING. 

Frictional Coupling. — Fig. 354 shows three views of 
Butler's frictional coupling. It is somewhat like the Sellers 
coupling, except that it has neither bolts nor keys, the conical 
bushes being held in position by round nuts threaded into the 
muff. The conical bushes are split at the side, and when they 
are in position on the shaft the split sides are at right angles 
to each other; this arrangement allows a key-driver to be 
introduced through one of these openings (after the nuts have 
been removed) to drive out the other bush when it is desired 
to remove the coupling from the shaft. The bushes are 
guided into position by small dowel-pins which enter short 
grooves provided for them inside the muff. The \" round 
holes shown in top and bottom at the centre of the muff are 
used to see when the ends of the shafts come together, for 
then only will the coupling be in its proper position. 

The threads on the lock-nuts should be that number per 
inch used on a pipe whose outside diameter is nearest to the 
outside diameter of the nut. The lock-nuts are screwed into 
position by means of a spanner wrench having projecting 
pieces which fit into the recesses shown in end elevation. 
The taper of the conical bushes may be made j-" in 12" on 
the diameter. The faces marked with small / are to be 
finished. 

The principal proportions of this coupling are as follows: , 

d = diameter of shaft; 
D = diameter of muff = 2.2 $d; 
' L = length of muff = 4^/. 



ELEMENTARY MACHINE DETAILS. 



269 




270 



MECHANICAL DRAWING. 



Stuart's Clamp Coupling.— This coupling, shown in Fig. 
355, differs from the Sellers coupling in having tapered 




wedges instead of conical sleeves; these tapered wedges and 
opposite halves of each end of the muff are bored to the size 
of the shaft. Studs and nuts hold the wedges in place, 
making, on the whole, a cheap and effective coupling without 
the use of keys. 

The principal dimensions of this coupling for various 
diameters of shaft are given in the following proportions: 
Let d = diameter of shaft; 
D ~ diameter of muff; 
L = length of muff. 
Then for shafts from ij" to 2|" diameter 
D = 3.2$d, L = 4.2$d; 

for shafts from 2f " up 

D = id, L = 4d. 



ELEMENTARY MACHINE DETAILS. 



271 




272 MECHANICAL DRAWING. 

Connecting-rods. — In steam and other engines the con- 
necting-rod connects the rotating crank with the reciprocat- 
ing cross-head. 

There are many styles of connecting-rods, and various 
methods are employed for taking up the wear of the brasses. 
Figs. 356 and 357 show good examples of rods used in station- 
ary, locomotive, and marine engines of the most modern 
types. 

Fig. 358 is the rod used by the Buckeye Engine Co. for 
their " Tangye " type of engine. The crank end is solid, the 
brasses are lined with babbitt, and adjustment for wear is had 
by means of a tapered steel block and screws. The cross- 
head end is called a strap end. The strap is firmly bound to 
the end of the rod with a cotter-key and gib, which also con- 
trols the adjustment for wear. 

Fig. 359 has strap ends front and back. Keys are in- 
serted between the straps and the rod to prevent the shear of 
the strap-bolts. The construction of this rod and the method 
employed to take up the wear are plainly shown in the figure. 
The Erie City Iron Works use this rod on their stationary 
engines. 

Exercise 132. — Make the drawings as shown in Fig. 358. 
(Scale 6" = 1 foot.) 

Exercise 133. — Make the drawings as shown in Fig. 359. 



ELEMENTARY MACHINE DETAILS. 



2 73 



rirt^rr 




274 



MECHANICAL DRAWING. 



TABLE 18. 



WIRE AND SHEET-METAL GAUGES COMPARED. 



* . 

it 


si* 


CO M 

ilg. 

^ 02 


Roebling's and 

Washburn 

& Moen's 

Gauge. 


Stubs' 

Steel Wire 

Gauge. 

(See also p. 29.) 


British Imperial 

Standard 

Wire Gauge. 

(Legal Standard 

in Great Britain 

since 

March 1, 1884.) 


U. S. Standard 

Gauge for 
Sheet and Plate 
Iron and Steel. 
(Legal Standard 
since July 1, 1893.) 






inch. 


inch. 


inch. 


inch. 


inch. 


millim. 


inch. 




0000000 






.49 




.500 


12.7 


.5 


7/6 
6/0 
5/0 


oooooo 






.46 




.464 


11.78 


.469 


00000 






.43 




.432 


10.97 


.438 


0000 


.454 


.46 


.393 




.4 


10.16 


.406 


4/0 


000 


.425 


.40964 


.362 




.372 


9.45 


.375 


3/0 


00 


.38 


.3648 


.331 




.348 


8.84 


.344 


2/0 





.34 


.32486 


.307 




.324 


8.23 


.313 





1 


.3 


.2893 


.283 


.227 


.3 


7.62 


.281 


1 


2 


.284 


.25763 


.263 


.219 


.276 


7.01 


.266 


2 


3 


259 


.22942 


.244 


.212 


.252 


6.4 


.25 


3 


4 


.238 


.20431 


.225 


.207 


.232 


5.89 


.234 


4 


5 


.22 


.18194 


.207 


.204 


.212 


5.38 


.219 


5 


6 


.203 


.16202 


.192 


.201 


.192 


4.88 


.203 


6 


7 


.18 


.144-28 


.177 


.199 


.176 


4.47 


.188 


7 


8 


.165 


.12849 


.162 


.197 


.16 


4.06 


.172 


8 


9 


.148 


.11443 


.148 


.194 


.144 


3-66 


.156 


9 


10 


.134 


.10189 


.135 


.191 


.128 


3.25 


.141 


10 


11 


.12 


.09074 


.12 


.188 


.116 


2.95 


.125 


11 


12 


.109 


.0S081 


.105 


.185 


.104 


2.64 


.109 


12 


13 


095 


.07196 


.092 


.182 


.092 


2.34 


.094 


13 


14 


.083 


.06408 


.08 


.180 


.08 


2.03 


.078 


14 


15 


072 


.05707 


.072 


.178 


.072 


1.83 


.07 


15 


16 


.065 


.05082 


.063 


.175 


.064 


1.63 


.0625 


13 


17 


.058 


04526 


.054 


.172 


.056 


!.42 


.0563 


17 


18 


.049 


0403 


.047 


.168 


.048 


1.22 


.05 


19 


19 


.042 


.03589 


.041 


.164 


.04 


1.02 


.0438 


19 


20 


.035 


.03196 


.035 


.161 


.036 


.91 


.0375 


20 


21 


.032 


02846 


.032 


.157 


.032 


.81 


.0344 


21 


22 


.028 


.02535 


.028 


.155 


.028 


.71 


.0313 


22 


23 


.025 


.02257 


.025 


.153 


.024 


.61 


.0281 


23 


24 


.022 


.0201 


.023 


.151 


.022 


.56 


.025 


24 


25 


.02 


.0179 


.02 


.148 


.02 


.51 


.0219 


25 


26 


.018 


.01594 


.018 


.146 


.018 


.46 


.0188 


26 


27 


.016 


.01419 


.017 


.143 


.0164 


.42 


.0172 


27 


28 


.014 


.01264 


.016 


.139 


.0148 


.38 


.0156 


28 


29 


.013 


.01126 


.015 


.134 


.0133 


.35 


.0141 


29 


30 


.012 


.01002 


.014 


.127 


.0124 


.31 


.0125 


30 


31 


.01 


.00893 


.0135 


.120 


.0116 


.29 


.0109 


31 


32 


.009 


.00795 


.013 


.115 


.0108 


.27 


.0101 


32 


33 


.008 


.00708 


.011 


.112 


.01 


.25 


.0094 


33 


34 


.007 


0063 


.01 


.110 


.0092 


.23 


.0086 


34 


35 


.005 


.00561 


.0095 


.108 


.0084 


.21 


.0078 


35 


36 


004 


.005 


.009 


.106 


.0076 


.19 


.007 


36 


37 




00445 


.0085 


.103 


.0068 


.17 


.0066 


37 


38 




.00396 


.008 


.101 


.006 


.15 


,0063 


38 


39 




.00353 


.0075 


.099 


.0052 


.13 




39 


40 




.00314 


.007 


.097 


.0048 


.12 




40 


41 








.095 


.0044 


.11 




41 


42 








.092 


.004 


.10 




42 


43 








.088 


.0036 


.09 




43 


44 








.085 


.0032 


.08 




44 


45 








.081 


.0028 


.07 




45 


46 








.079 


.0024 


.06 




46 


47 








.077 


.002 


.05 




47 


48 








.075 


.0016 


.04 




48 


49 








.072 


.0012 


.03 




49 


50 

1 








.069 


.001 


.025 


■ 


50 



ELEMENTARY MACHINE DESIGN. 



275 





DIFFERENT 


Cent. 


Fahr. 


2IO° 


4IO° . 


221 


430 . 


256 


493 • 


26l 


502 ) 
680 \ 


370 



500 



932 



525 


977 


700 


1292 


800 


1472 


900 


1657 


1000 


1832 


IIOO 


2012 


1200 


2192 


1300 


2372 


1400 


2552 


1500 


2732 


1 600 


2912 



TABLE 19. 

COLORS OF IRON CAUSED BY HEAT. (Pouillet.) 
Color. 
. . . Pale yellow. 
. . . Dull yellow. 
. . . Crimson. 

. . . Violet, purple, and dull blue; between 261° C. 
and 370 C. it passes to bright blue, to sea- 
green, and then disappears. 
. . . Commences to be covered with a light coat- 
ing of oxide; loses a good deal of its 
hardness, becomes much more impressible 
to the hammer, and can be twisted with 
ease. 
. Becomes nascent red. 
. Sombre red. 
, Nascent cherry. 
. Cherry. 
. Bright cherry. 
. Dull orange. 
. Bright orange. 
. White. 

. Brilliant white — welding heat. 
Dazzling white. 



TABLE 20. 

TABLE OF DECIMAL EQUIVALENTS OF ONE INCH. 



1/64 


.015625 


17/64 


.265625 


33/64 


•515625 


49/64 


765625 


1/32 


.03125 


9/32 


.28125 


17/32 


•53125 


25/32 


78125 


3/64 


.046875 


19/64 


.296875 


35/64 


.546875 


51/64 


796875 


1/16 


.0625 


5/i6 


.3125 


9/16 


•5625 


13/16 


8125 


5/64 


.078125 


21/64 


.328125 


37/64 


.578125 


53/64 


828125 


3/32 


•09375 


11/32 


•34375 


19/32 


•59375 


27/32 


84375 


7/64 


•109375 


23/64 


•359375 


39/64 


.609375 


55/64 


859375 


1/8 


.125 


3/8 


•375 


5/8 


.625 


7/8 


875 


9/64 


. 140625 


25/64 


.390625 


41/64 


.640625 


57/64 


890625 


5/32 


.15625 


13/32 


.40625 


21/32 


•65625 


29/32 


90625 


11/64 


.171875 


27/64 


.421875 


43/64 


.671875 


59/64 


921875 


3/i6 


.1875 


7/16 


•4375 


11/16 


.6875 


15/16 


9375 


13/64 


.203125 


29/64 


.453125 


45/64 


.703125 


61/64 


953125 


7/32 


.21875 


15/32 


.46875 


23/32 


.71875 


31/32 


96875 


15/64 


234375 


31/64 


.484375 


47/64 


•734375 


63/64 


984375 


1/4 


.25 


1/2 


.50 


3/4 


• 75 


z 





276 MECHANICAL DRAWING. 

TABLE 21. 

CIRCUMFERNCES AND AREAS OF CIRCLES ADVANCING BY EIGHTHS. 



Diam. 


Circum. 


Area. 


Diam. 


Circum. 


Area. 


Diam. 


Circum. 


Area. 


1/64 


.04909 


.00019 


2 11/16 


8.4430 


5.6727 


6 5/8 


20 813 


34-472 


1/32 


.09818 


.00077 


3/4 


8.6394 


5 939 6 


3/4 


21.206 


35-785 


, 3/64 


.14726 


.00173 


13/16 


8.8357 


6.2126 


7/8 


21.598 


37.122: 


1/16 


.19635 


.00307 


7/8 


9.0321 


6.4918 








3/32 


.29452 


.00690 


I5A6 


9.2284 


6.7771 


7 


21.991 


38.485 


1/8 


.39270 


.01227 








1/8 


22.384 


' 39-87I 


5/32 


.49087 


.01917 


3 


9.4248 


7.0686 


i/4 


22.776 


41.282 


3A6 


.58905 


.02761 


1/16 


9. 62 1 1 


7. 3662 


3/8 


23.169 


42.718 


7/32 


.68722 


•03758 


1/8 


9.8175 


7.6699 


1/2 


23.562 


44-179 


1/4 


.78540 


.04909 


3/^6 


10.014 


7.9798 


5/8 


23-955 


45.664 


9/32 


.88357 


.06213 


1/4 


10.210 


8.2958 


3/4 


24-347 


47-173 


5/16 


•98175 


.07670 


5/i6 


10.407 


8.6179 


7/8 


24.740 


48.707 


11/32 


1.0799 


.09281 


3/8 


10.603 


8.9462 








3/8 


1. 1781 


.11045 


7/16 


10 799 


9.2806 


8 


25-133 


50.265 


13/32 


1.2763 


.12962 


1/2 


10.996 


9.6211 


1/8 


25-525 


51849 


7/16 


1-3744 


.15033 


9/16 


11 . 192 


9.9678 


1/4 


25.918 


53456 


is/32 


1.4726 


•17257 


5/8 


n.388 


10.321 


3/8 


26 .311 


55 088 


1/2 


1.5708 


•19635 


11/16 


"■585 


10.680 


1/2 


26.704 


56.745 


17/32 


1 . 6690 


.22166 


3/4 


11. 781 


11.045 


5/8 


27.096 


58.426 


9/16 


1. 7671 


.24850 


13/16 


11.977 


11. 416 


3/4 


27.489 


60.132 


*9/32 


1.8653 


.27688 


7/8 


12.174 


"•793 


7/8 


27.882 


61.862 


5/8 


1.9635 


. 30680 


15/16 


12.370 


12.177 








21/32 


2.0617 


•33824 








9 


28.274 


63.617 


11/16 


2.1598 


.37122 


4 


12.566 


12.566 


1/8 


28.667 


65.307 


23/32 


2.2580 


•40574 


1/16 


12.763 


12.962 


1/4 


29 . 060 


67.201 


3/4 


2.3562 


.44179 


1/8 


12.959 


13-364 


3/8 


29.452 


69 . 029 


25/32 


2-4544 


•47937 


3/i6 


13-155 


13-772 


1/2 


29.845 


70.882 


13/16 


2.5525 


.51849 


i/4 


'3-352 


14.186 


5/8 


30.238 


72 . 760 


27/32 


2.6507 


•559H 


5A6 


13-548 


14.607 


3/4 


30.631 


74.662 


7/8 


2.7489 


.60132 


3/8 


13-744 


15.033 


7/8 


31.023 


76.58P 


29/32 


2.8471 


.64504 


7/16 


i3-94i 


15.466 








15/16 


2-9452 


.69029 


1/2 


14-137 


15.904 


10 


31.416 


78.540 


31/32 


3.0434 


•737o8 


9/16 


14-334 


16.349 


1/8 


31.809 


80.516 








5/8 


14-530 


16.800 


1/4- 


32.201 


82.516 


I 


3.1416 


.7854 


11/16 


14 726 


17-257 


3/8 


32-594 


84-54I 


1/16 


3-3379 


.8866 


3/4 


14-923 


17.721 


1/2 


32.987 


86.590 


1/8 


3-5343 


.9940 


13/16 


15-119 


18.190 


5/8 


33-379 


88.664 


3/i6 


3-73o6 


1.1075 


7/8 


15-315 


18.665 


3/4 


33-772 


90.763 


x/4 


3.9270 


1.2272 


15/16 


15-512 


19.147 


7/8 


34-i65 


92.886 


5/i6 


41233 


1-353° 














3/8 


4-3I97 


1.4849 


5 


15.708 


19. 6 35 


11 


34-558 


95-033 


7/16 


4.5160 


1.6230 


1/16 


15-904 


20.129 


1/8 


34-950 


97 • 205 


1/2 


4.7124 


1.7671 


1/8 


16.101 


20.629 


1/4 


35-343 


99.402 


9/16 


4.9087 


1. 9175 


3/16 


16.297 


2i.i35 


3/8 


35-736 


101.62 


5/8 


5.1051 


2.0739 


x/4 


16.493 


21.648 


1/2 


36.128 


103.87 


Il/l6 


5-30I4 


2.2365 


5/i6 


16.690 


22. 166 


5/8 


36.521 


106.14 


3/4 


5-4978 


2.4053 


3/8 


16.886 


22.691 


3/4 


36.914 


108.43 


13/16 


5.6941 


2.5802 


7/i6 


17.082 


23.221 


7 /8 


37-3°6 


110.75 


7 /8 


5.8905 


2.7612 


1/2 


17.279 


23-758 








15A6 


6.0868 


2.9483 


9/16 


17-475 


24.301 


12 


37-699 


113.10 








5/8 


17.671 


24.850 


1/8 


38.092 


"5-47 


3 


6.2832 


3.1416 


ji/i6 


17.868 


25.406 


1/4 


38.485 


117.86 


1/16 


6.4795 


3-34IO 


3/4 £ 


18.064 


25.967 


3/8 


38.877 


120.28 


1/8 


6.6759 


35466 


13/16 


18.261 


26.535 


1/2 


39-270 


122.72 


3/16 


6.8722 


37583 


7/8 


18.457 


27.109 


5/8 


39663 


125.19 


1/4 


7.0686 


3.9761 


15/16 


18.653 


27.688 


3/4 


40.055 


127.68 


5/i6 


7.2649 


4.2000 








7/8 


40.449 


130.19 


3/8 


7-4613 


4.4301 


6 


18.850 


82.274 








7/i6 


7.6576 


4.4664 


1/8 


19.242 


g9-465 








1/2 


7.8540 


4.9087 


1/4 


I9.635 


30.680 








9/16 


8.0503 


5.I572 


3/8 


20.028 


31-919 








5/8 


8.2467 


5-4II9 


1/2 


20.420 


33183 









To find the weight of castings by the weight of pine patterns, multiply the 
weight of the pattern by 12 for cast iron, 13 for brass, 19 for lead, 12.2 for tin, 
14.4 for zinc, and the product is the weight of the casting. 



COURSE II. 

PROBLEMS IN 
ADVANCED MECHANICAL DRAWING 

INCLUDING 

ISOMETRICAL DRAWING, ARCHITECTURAL DRAW- 
ING, SHEET METAL DRAFTING, MACHINE DE- 
TAILS, FREEHAND SKETCHING OF SMALL MA- 
CHINE PARTS AND WORKING DRAWINGS OF 
SAME. 



277 



COURSE II. 
ADVANCED MECHANICAL DRAWING. 

MINIMUM NUMBER OF PLATES AND MAXIMUM NUM- 
BER OF HOURS ALLOWED TO COMPLETE EACH 
DIVISION OF THE WORK. 

FIRST SEMESTER. SIX HOURS PER WEEK. 

Plate 22. Isometrical Drawing, to be handed in Sept. 24, 1909. 

(14 hours.) 
Plates 23 to 26 inclusive, Architectural Drawing, to be handed 

in November 12, 1909. (42 hours.) 
Plates 27 to 29 inclusive, Sheet Metal Drafting, to be handed 

in December 17, 1909. (30 hours.) 

SECOND SEMESTER. SIX HOURS PER WEEK. 

Plate 30. Sheet Metal Drafting, to be handed in January 14, 

1 910. (12 hours.) 
Plates 31 to 1,1, inclusive, Machine Details, to be handed in 

March 11, 1910. (42 hours.) 
Plates 34 and 35, Freehand Sketches of small Machine parts 

and Working drawings of same. (60 hours.) 

Total, 200 hours. 

279 



280 MECHANICAL DRAWING. 

Isometrical Drawing. 

Plate 22. Make freehand sketches of (1) Library Book Trans- 
ferring Shelves (2) Drafting Table, and (3) a twelve drawer 
section of Drafting Room Lockers. These sketches are to 
be made on an isometric paper pad with dimensions and title. 
When sketches have been approved and signed, a finished 
pencil working drawing is to be made. 

Architectural Drawing. 

Plate 23. Make finished pencil drawing of framing joints as shown 
in Figs. 220-233 on Whatman's cold pressed white paper. 
When approved and signed this plate is to be inked and 
tinted in water colors. 

Plate 24. Make finished pencil drawing of brick and stone work 
shown in Figs. 234-240 on cream detail paper. W T hen 
pencil drawing has been approved and signed, it is to be 
traced on cloth and blue printed. 

Plate 26. Make finished pencil drawing of the examples of 
Tuscan and Doric Orders of Architecture as shown in Figs. 
243 and 244 on Whatman's cold pressed white paper. When 
pencil drawing is approved and signed, it is to be inked 
and the shaded and sectioned parts are to be tinted with a 
light wash of India ink. 

Plate 28. Make finished pencil drawing of the example of the 
Ionic Order of Architecture as shown in Figs. 247 and 248 on 
Whatman's cold pressed white paper. When the pencil 
drawing is approved and signed, it is to be inked and the 
sectioned parts are to be tinted with a light wash of India ink. 



PROBLEMS IN ADVANCED MECHANICAL DRAWING. 281 

Plate 25. Make drawing of the Classic Renaissance Letters, 
Figs. 241 and 242. One alphabet 1" high and alphabets of 
lesser height to fill one plate. Directions to be given by 
Instructor. This plate may be made at odd hours during 
the semester. 

Sheet Metal Pattern Drawing. 

Plate 29. Make pattern drawings of objects as shown in Figs. 
276 to 288 inclusive, according to directions given on page 
216. 

Plate 30. Make pattern drawings of objects shown in Figs. 289 
to 296 inclusive, according to directions given on page 218. 

Plate 31. Make pattern drawings of articles shown in Figs. 297 
to 310 inclusive, according to directions given in pages 223 to 



22 



Plate 3 2. Draw the developments of pipe elbows as given in 
Figs. 311 to 314 according to directions given on page 226. 

Machine Drawing. 

Plate 33 . 

Prob. 1. Draw the U. S. standard or Sellers' V-threads, 
Fig. 360, suitable for a screw 6" in diameter. Scale three times 
full size. 

See Table 1 for the value of p, the pitch of the screw, d is 
the nominal diameter of the screw, d x the effective diameter of the 
bolt, and n the number of threads per inch. 

Prob. 2. Draw 2 \ threads of the "Whitworth," or English 
standard V-thread, Fig. 361, for 6" screw. Scale three times 
full size. 



282 MECHANICAL DRAWING. 

Prob. 3. Draw the sectional outline of the square, knuckle 
and buttress shown in Figs. 362 and 363, respectively. p=i" 
Scale, full size. 

Prob. 4. Draw the section of a pipe screw, Fig. 364, for a 
wrought iron pipe 8" in diameter. Scale, three times full size. 
See Table 2 for the number of threads per inch, the taper of the 
screw and the thickness, t, of the pipe. 

Prob. 5. Make drawings of the screw thread conventions 
shown in Fig. 365. Scale, full size. 

(1) is a right-hand double V-thread U. S. standard d=i". 

(2) is a right-hand single V-thread U. S. standard d=\". 

(3) is a right-hand single square thread U. S. standard 

rf=i". 

(4) is left-hand single V-thread U. S. standard d=i". 

(5) is a right-hand double square thread U. S. standard 
d=i". 

(6) is a right-hand single V-thread U. S. standard d=%". 
In the double thread the screw advances two pitches in each 

revolution, therefore the inclination of the thread is equal to 
the pitch. (6) is the standard convention used to represent 
threads on the common sizes of bolts and nuts. 

Prob. 6. Draw the projections of a hexagonal nut, Fig. 366, 
for a bolt whose diameter d is equal to 1". Scale, full size. 

F=i\d+\". D=FXi.iSS- H=d - 

Construct the plan first. Draw the chamfer circle F and 
circumscribe a hexagon about it with the 30°X6o° triangle and 
T-square. Project elevation and end elevation from the plan. 

Prob. 7. Draw the projections of a square nut, Fig. 367, 
for a 1" bolt. Scale, full size. 

As in the last problem draw the plan first and project the 



PROBLEMS IN ADVANCED MECHANICAL DRAWING. 28 




284 MECHANICAL DRAWING. 

elevations from it. A square nut should never be shown in 
elevation across the corners. 

Prob. 8. Make drawings for 1" bolt with castle nut, Fig. 368. 
Scale, full size. 

The values of the letters in the figure are to be taken from 
Table 3 which gives the standard proportions adopted by the 
American Licensed Automobile Manufacturers. Use the same 
proportions for drawing the chamfer curves on the elevations as 
given for the U. S. standard nut. Make the saw cut in the head 
.2d in width and the depth equal to ij times the width. 

Prob. 9. Make drawings of the rectangular keys and their 
connections shown in Fig. 370. Diameter of shaft D in No. 15 
is equal to \" '. Scale, full size. Diameter of shaft in No. 16 is 
equal to 2". Scale, 6"=i foot. Take the key dimensions from 
Tables 5 and 6. 

Prob. 10. Make drawings of the tension and compression 
springs shown in Figs. 371 and 372. Scale, full size. 

Fig. 372 is a compression spring and spindle for a boiler safety 
valve. See model in drafting room. 

Prob. ii. Make drawing of split pin shown in Fig. 369. Scale, 
full size. Assume D = ^ r , and d =.o$D + .13. 

The split pin is made from half round wire which when pressed 
into form gives a circular cross-section. 

Selections from the following problems may be made to 
Conveniently fill the space in Plate 34, allowing for title and bill 
of material. 

Plate 34. 

Prob. i. Make drawing for a 2^-ton crane-hook, Fig. 379. 
Scale, 6" = 1 foot. Find values for the different letters in Table 15. 



PROBLEMS IN ADVANCED MECHANICAL DRAWING- 2S5 



< 




286 MECHANICAL DRAWING. 

Prob. 2. Make the drawings of a cotter joint, Fig. 374. Scale, 
full size. Taper of cotter is \" per foot. 

Prob. 3. Make drawings of a nut wrench to dimensions 
given in Fig. 375. Scale, full size. For other sizes of wrenches 
see Table 7. 

Prob. 5. Make drawings of a gib and cotter to dimensions 
given in Fig. 327. Scale, 3"= 1 foot. S is the strap, B the brasses, 
C the cotter, G the gib, R the connecting rod, and X the set screw. 

Prob. 6. Draw the " Woodruff" key, Fig. 373, for a i\ n 
shaft. Take dimensions from Table 8. 

Prob. 7. Draw the ball crank handle, Fig. 378, to the dimen- 
sions given. Scale, full size. 

Prob. 8. Make drawings of chain and link and narrow 
shackle, Fig. 377. Scale, 4"=i foot. Take dimensions from 
Table il 

Prob. 9. Make drawing of taper pin, Fig. 64. Scale, full 
size. Taper of pin is \" per foot. The finish curves at the end 
are made with a radius equal to the diameter. The material 
is steel. 

Prob. 10. Make drawing of hand wheel, Fig. 65, outside 
diameter 6". Scale, 6" = 1 foot. Take remaining dimensions 
from Table 9. 

Prob. ±i. Make drawings of a washer for a i|" bolt. Take 
dimensions from Table 13. See Fig. 379. 

Prob. 12. Make drawings of cast-iron flanges shown in Figs. 
374 and 376 for a 1" bolt. Scale, 6"=i foot. 

Prob. 13. Make working drawing of hand wheel, Fig. 381, 
6" diameter. Scale, 6"=i foot. 

Prob. 14. Make working drawing of shaft collar, Fig. 382; 
for a 2" shaft. Scale, full size. 



PROBLEMS IN ADVANCED MECHANICAL DRAWING. 287 

Machine Detail Sketches. 
Plates 35 and 36. 

These plates are to contain certain machine parts to be applied 
to the student by the instructor. Each object is to be sketched 
in orthographic projection on an 8X10" sheet of cross-section 
paper with a 4H pencil. Use only one side of the paper. Sketch 
three views of each piece, viz., the elevation, plan, and right end 
view. All dimensions, notes, title, and finish marks must be 
neatly placed on the sketch. 

Begin by drawing all the center lines for the front and end 
elevations and the plan. Make size of sketch to suit size of paper. 
Lines should be sketched very lightly and when sketch is approved 
and signed in pencil, the lines may be strengthened. 

Put on all dimension lines before measuring the object. 
Measure with the two-foot rule and callipers. Callipers may be 
borrowed from the Instructor. 

Sufficient dimensions must be placed on the sketch to enable 
the draftsman to make a working drawing for the pattern maker 
without having recourse to the object, after the drawing is com- 
menced. 

When a sufficient number of sketches have been made to rill 
one sheet of the usual size 15X20", working drawings are to be 
made in finished pencil drawings. The finished pencil drawing 
must carry all dimensions, notes, finish marks, title, bill of material, 
and when approved and signed by the instructor it is to be traced 
on tracing cloth and blue printed. 



PRESENT PRACTICE IN DRAFTING ROOM 
CONVENTIONS AND METHODS IN MAKING 
PRACTICAL WORKING DRAWINGS. 



Summary Report of an Investigation made by the Writer 
with the Authority of the Armour Institute of 
Technology. Chicago, III., into the Present Prac- 
tice OF THE LEADING DRAFTSMEN IN THE UNITED STATES, 
IN THE USE OF STANDARD CONVENTIONS AND METHODS 
WHEN MAKING COMMERCIAL WORKING DRAWINGS. 

A circular letter accompanied by a list of thirty-five questions 
was submitted to two hundred leading firms in the United States 
embracing nearly all kinds of engineering practice. 

The returns have been exceedingly gratifying, and especially 
so has been the spirit with which the " Questions" have been 
received and answered. 

Many requests have been received from chief draftsmen for 
a copy of the returns. 

The questions submitted and the answers received are given 
somewhat in detail below. 



290 MECHANICAL DRAWING. 

Q. 1. Do you place complete information for the shop on the 
pencil drawing, such as all dimensions, notes, title, bill of 
material, scale, etc. ? 

Complete information is placed on drawing before tracing. 57 

Complete information is placed on tracing only 42 

Principal dimensions and title only on pencil drawing 2 

Draw directly on bond paper 10 

Did not answer this question 10 

Sometimes 7 

Reasons given for making the pencil drawing complete: 

To arrange notes. To save ime. The tracing is not usually 
made by the draftsman who makes the pencil drawing. 

Q. 2. Do you ever ink the pencil drawing? 

Never ink the pencil drawing 91 

Generally ink the pencil drawing 7 

Sometimes ink the pencil drawing 8 

Sometimes ink the pencil drawing and shellac it for shop use . 1 

Use bond paper 10 

Make pencil drawings on dull side of tracing cloth 2 

Ink center lines of assembly drawing 1 

Ink center lines of pencil drawings in red 2 

Q. 3. Do you trace on cloth and blue print? 

Always trace on cloth and blue print 102 

Blue print from bond paper * 10 

Blue print from bond paper occasionally 1 

Sometimes make " Vandyke " prints for shop use 1 

Sometimes use paper drawings in shop for jigs and fixtures . 1 

Q. 4. Do you use blue prints entirely in the shop? 

Use blue prints altogether in shop 105 

Sometimes use pencil drawings or sketch 21 



PRESENT PRACTICE IN DRAFTING ROOM CONVENTIONS. 291 

Sometimes use sketches made with copying ink 

Sometimes use prints from " Vandyke " 

Use white prints mounted on cardboard and varnished 

Use blue prints mounted on cardboard , 

Use sketches for rush work 

Q. 5. When tracing do you use uniform wide object lines ? 
Ever use shade lines? 

Use uniform, thick object lines. Never use shade lines 100 

Sometimes use shade lines 21 

Use shade lines on small details 5 

Always use shade lines 14 

Experts in the use of shade lines may do so to make drawings 

clear 1 

Shade rounded parts 1 

Q. 6. What kind of a center line do you use ? 

Long dash, very narrow, and dot, thus : 42 

Long dash and two dots, 29 

Very fine continuous line, 19 

Very fine dash line, long dashes, 8 

Long dash and dot in red, 3 

Continuous fine red line, 8 

Long dash and three dots, 1 

Long dash and two dots, thus: ] | 1 

Q. 7. What kind of dimension line do you use ? 

Continuous fine line, broken only for dimension ■ 52 

Fine long dash line, ■ 32 

Fine long dash line and dot, 13 

Fine continuous red line, ■ — 8 

F : ne continuous blue line, 4 

Fine continuous green line, 1 



292 MECHANICAL DRAWING. 

Same character of line as center line, 2 

Dotted line, - -- 1 

Long dash and two dots, ■ 2 

Heavy broken lines, 1 

Q. 8. What style of lettering do you use ? Sloping ? Vertical ? 
Free-hand? All capitals of uniform height? or capitals 
and lower case ? 

Free-hand sloping 52 

Free-hand vertical 45 

Free-hand capitals, Gothic, uniform height 61 

Free-hand capitals, and lower case 40 

All caps, initials slightly higher 5 

Lettering left to option of draftsman 2 

Mechanical lettering, all caps 3 

Not particular, the neatest the draftsman can make free- 
hand 4 

Mechanical lettering, all caps, sloping 2 

Give great latitude in lettering, only insist it be bold and neat 1 

Roman, caps and lower case, free hand 2 

Large letters i^ths, small -^ds and Jth 2 

Q. 9. Are your titles and bills of material printed or lettered by 
hand ? 

Lettered by hand 79 

Standard titles printed and filled in by hand 12 

Bill of material table printed and lettered by hand 12 

Lettered by hand, contemplate having them printed 1 

B. of M. typewritten on separate sheet and blue printed... 8 

Titles partly printed and filled in by hand 8 

Use rubber stamp for standard title, fill in by hand 6 

Standard title, bill of material lithographed on tracing 

clem 8 



PRESEXT PRACTICE IN DRAFTING ROOM CONVENTIONS. 293 

Q. 10. Do you use a border line on drawings? 

Always use border lines 97 

Never use border lines 13 

Use border lines on foundation plans, to send out 

No border lines on detail drawings 

Intend to discontinue the use of border lines 

Border lines used only on design drawings 

Only on drawings to be mounted on cardboard 

Only used for trimming blue print 2 

On assembly drawings only 1 

Width of margins reported: 1", \" , f", J", and \" . 

Q. 11. When hatch-lining sections, do you use uniform or 
symbolic hatch lines ? 

Standard symbolic lines 59 

Uniform hatch lines for all materials . , 44 

Shade section part with 4H pencil and note name of material 4 

Symbolic hatch lines and add name of material 3 

Uniform hatch lines for metal only 1 

Uniform on details, symbolic on assembly drawings 5 

Pencil hatch on tracings and note material other than cast 

iron 1 

Uniform hatch lines, sometimes solid shading 1 

No uniform system 1 

Sections tinted with water colors representing the metals.. 1 

Q. 12. Is the pencil drawing preserved? Is the tracing 
stored or do you make "Vandyke" prints for storing away? 

Store tracings only 96 

Pencil drawings preserved for a time 30 

Pencil drawings preserved 13 

White prints made and bound for reference 1 

Tracings kept in office for reference, blue prints stored.... 9 

" Vandyke " prints stored 1 



294 MECHANICAL DRAWING. 

Use "Vandyke" as substitute for tracing 2 

Arrangement drawings preserved, detail drawings destroyed 
after job is completed. Pencil drawings used for gasket 

paper 1 

Original pencil drawing inked and stored 1 

Assembly drawings and layouts preserved 4 

Patent office drawings preserved - 1 

Tried " Vandyke " but found it unserviceable, tearing easily. 1 

Q. 13. Do you use 6H grade of pencil for pencil drawings or 
what? 

6H 73 

4H, mostly for figures and letters 52 

5H 16 

Ranging from 2H to 8H 53 

Q. 14. Do you use plain orthographic projection for free-hand 
sketches? Ever use perspective or isometrical drawing for 
sketches ? 

Plane orthographic 3d angle projection 99 

Isometrical drawing for sketches 25 

Perspective for sketches 1 

Isometric for piping layouts and similar work 8 

Perspective and isometric for catalogue work 2 

Isometric sometimes 6 

Never use free-hand sketches 6 

One says, "When we run into other than orthographic, men are 
too timid and not sure of themselves. In perspective drawings when 
work is cylindrical, workmen get mixed up on center lines. 

Q. 15. What sizes of sheets do you use for drawings? 

9"Xi2" 13 

12" X 18" 16 



PRESENT PRACTICE IN DRAFTING ROOM CONVENTIONS. 295 

l8"X24"... - - - 20 

2 4 "X36" - -- 19 

There seems to be little uniformity in the sizes of shop drawings, 
about 67 firms reporting different combinations. A few have no 
system but simply make the size of sheet to suit the object to be 
drawn. 

Q. 16. Do you use red ink on tracings? 

Never use red ink on tracings 57 

Recently discarded the use of red ink 2 

Use red ink for pattern figures 1 

Use red ink for center and dimension lines 8 

Use red ink for check marks 1 

Use red ink for existing work on studies 1 

Use red ink sometimes 2 

Use red ink on occasions when it is desired to show old work 

in red and new work in black (use carmine) 1 

Use carmine for brick 1 

Qs. 17 and 27. How indicate finished surfaces on drawings? 
When finished all over? When "file finished," ground, 
planed, bored, drilled, etc. ? 

Finished surfaces indicated as in Fig. 1 65 

Finished surfaces indicated as in Fig. 2 16 

Finished surfaces indicated as in Fig. 3 8 

Finished surfaces indicated as in Fig. 4 2 

Finished surfaces indicated as in Fig. 5 2 

Bound the surfaces with red lines 2 

Bound the surfaces with dotted lines 2 

Name the finish by note in full 68 

Do not specify machinery method 6 

(See drawing.) 



296 



MECHANICAL DRAWING. 



Q. 18. Do you use horizontal or sloping lines for convention 
in screw threads ? 

Sloping lines, see Fig. 6 94 

Horizontal lines, see Fig. 7 12 



/F 



■#■ 



/=/A/. 



/=/G. A 



X. 



m 



3 



»« A HZ 



m 



Finish only third line from top 

" L-f 



y 



1 

^-^ 



Fig. 6. 




^y ^ 




ri 



Fig. 7. 



Fig. 8. 






Fig. 9. 




Horizontal lines, see Fig. 8 
Both 



Fig. 10. 
... 13 



Neither, but as shown in Fig. 9 1 

Neither, but as shown in Fig. 10 1 



PRESENT PRACTICE IN DRAFTING ROOM CONVENTIONS 2 



97 



Q. 19. When a large surface is in section do you hatch-line 
around the edges only? 

Hatch-line edges only 6 2 

Sometimes 

Hatch section all over 

Do not use hatch lines; shade the whole surface with 4H 

pencil ^ 

Usually show a broken surface line ! 



3 

54 




F/G.J/. 



&GJ2. 



Q. 20. Do you section keyways in hubs or show by invisible 
lines ? 

Section keyways as shown in Fig. 11 *, 

Show key way by invisible lines, see Fig. 12 4 o 

Keyways in hubs left blank T 



Q. 21. In dimensioning do you prefer to place the dimension 
upon the piece or outside of it ? 
Outside whenever possible o 2 



Upon the piece. 



13 



298 MECHANICAL DRAWING. 

Both, according to size and shape of part 19 

No rule „ 1 

Commenting on placing dimensions outside of piece one says, 
"It entails less confusion to workman." Another says: "So as to 
make detail stand out." 

Q. 22. Do you use feet and inches over 24 inches? 

Yes 69 

Use feet and inches over 36" 4 

Use feet and inches over 24" on foundations and outlines . . 2 

Use feet and inches over 48" 6 

All inches ...... 21 

For pulleys use inches up to 48" 1 

Inches up to 10 feet 2 

Start feet at 24" thus : 2—0" 2 

Usually, but not always 2 

Yes, except pitch diameters of gears, which are all given in 

inches 2 

Yes, except in boiler and sheet iron work 3 

Use feet and inches over 12" 6 

Inches up to 100" 3 

Inches up to 60" 1 

Q. 23. How do you indicate feet and inches? Thus 2 ft. 4", 
or thus 2—4"? 

2-4"— 97, 2"' 4"— 5,2 *T. 4"— 2, 2ft. 4"— 13. Both 2ft. 4" 

and 2-4" — 1, 2FT. 4 in. — 1, 2' 4" — 8, 2-4" — 1. 

Q. 24. Do you dimension the same part on more than one view ? 

One view 94 

More than one view as check 46 



PRESENT PRACTICE IN DRAFTING ROOM CONVENTIONS. 299 

Q. 25. When several parts of a drawing are identical would the 
dimensioning of one part suffice for all, or would you repeat 
the dimension on each part? 

One part only 82 

Would repeat or indicate by note 39 

" Left to judgment of draftsman " 1 

" When it is evident that several parts are identical the dimensioning 
of one part would suffice, 'Would never leave room for doubt.'" 

Q. 26. Do you write R for radius or rad. ? D. for diameter 
or dia. ? 

rad . . 35 Rad . . .47 R .... 32 rad. . . 1 r 3 

dia . . 41 Dia . . 48 D. ... 15 d . . . . 3 dia ... 4 
diam .... 1 Diam. ... 3 diam 5 

Do not use R. or rad., dimension only 1 

Q. 28. Do you always give number of threads per inch? 
When you do how are they indicated ? 
Only give number of threads when not standard 67 

All others always indicate number of threads in a great variety of 
ways. A few of the different styles of noting the threads are given 
below : 

}" — 10 Thr. 5THDS. per 1". 8thds. 4 threads per inch. Mach. 
Screw 10-24, i\" XII, 16 P. RH. Vth. U. S. S. XVIII, i"-8- 
U. S. S. i" TAP, 8 pitch, 3 th'd r. h. sq. double, 5"-i8 
thds. r. h. own st'd io thds. per inch. For pipe tap thus 
\" p.t., etc., etc. 

Q. 29. How do you "Mark" a piece to indicate on the bill of 
material ? 

Number it on drawing and put a circle around it 34 



300 . MECHANICAL DRAWING. 

By name or letter ' 35 

By pattern number 2 

By symbol and number ; . . 14 

Castings, I, II, III, Forgings, 1, 2, 3. 

Q. 30. When a working drawing is fully dimensioned why 
should the scale be placed on the drawing ? 

For convenience of drafting room 25 

Check against errors 11 

Not necessary 18 

Scale not placed on shop drawings 18 

For convenience in calculations and planimeter work 1 

To give an idea of over-all dimensions when these are not 
given. " We never saw a drawing so fully dimensioned 

as to warrant leaving off the scale " 2 

" If a drawing is to scale the scale should be on the drawing, whether 
it is needed or not." 

" It gives every one interested a better conception of the proportions 
of the piece, and there are frequently portions" of a design which do 
not require a dimension for the shop to work to, and which it is 
interesting to scale from an engineering point of view." 

"To get approximate dimensions not given on drawing." 

"Impractical to dimension all measurements for all classes of 
work." 

"Scale will tell at a glance, dimensions would have to be 
scaled." 

"To obtain an idea of relative size of parts without scaling the 
drawings." 

"To sketch on clearance." "To proportion changes." "When 
erecting to measure over-all sizes." 

" In case a dimension has been left off, the scale will help out." 

"This is a question of opinion; some will not have the scale, others 
insist on. it." "We always give the scale." 



PRESENT PRACTICE IN DRAFTING ROOM CONVENTIONS. 301 

"It is an immense help and time saver fn the drawing room." 

11 Generally no reason. In our work we combine standard apparatus 
by 'fudge' tracing, and it is convenient to know scale so all parts will 
surely be to same scale." 

"In discussing alterations, additions, clearances, etc., it is con- 
venient to know the scale instantly." 

"For convenience in drafting room. We often put an arbitrary 
scale on with a reference letter indicating scale to draftsman." 

"To give toolmaker an idea of the size of the finished piece." 

"As an aid to the eye in reading." 
Above are some of the reasons given for placing the scale on the 

drawing. Below are given a few of the reasons why some do not 

place the scale on the drawing. 

" Scale should never be used in shop," says one. 

"Not necessary. Sometimes drawing is made out of scale." 

" Not advisable, on account of workmen getting into the habit of 
working to scale instead of to the figures.'' 

"Know of no good reason at all." 

"Believe it best to leave scale off." 

" Should not. Drawing should never be scaled." 

"Know of no good reason why it should be." 

" Should not be given on drawing." 

"Do not object if left off, not needed." 

Q. 31. Do you use the glazed or dull side of tracing cloth? 
Dull side... 66 Glazed side. 32 Both 4 

"Dull side, because it lies flat better in drawers." 

" Dull side, so that changes which may be necessary while work is 
under construction, can be made easily in pencil and later in ink." 

"Dull side so tracings may be checked in pencil." 

"It prevents curling." 

" Both, although the glazed side, when traced on lies better in the 
drawer." 



302 MECHANICAL DRAWING. 

"We use cloth glazed on both sides, work on convex side, so that 
shrinkage of ink will eliminate camber." 

" Dull, except for U. S. Government, who requires the glazed side 
to be used." 

Q. 32. How do you place pattern numbers on castings? 

Pattern number with symbol or letter is placed on or near 
the piece, e.g., PATT.-D-478-C 36 

This question was not happily stated : most answers gave " raised 
letters cast on," while the question like all the others refers to the 
marking of the drawing. 

Q. 33. How do you note changes on a drawing? 

On tracing with date 32 

New tracing and new number 17 

Put a circle around old figure and write new figure beside 

it with date 8 

Make new tracing OB 5 

Red ink with date 8 

Use rubber stamp " Revised" with date, and indicate changes 

on record print 28 

Use change card system 1 

Special forms for purpose. Change made in a book with 

date. New prints made to replace. In place at title 

with draftsman's initials and date 8 

Q. 34. Do you place dimensions to read from bottom and 
right hand, or all to read from bottom, or how ? 

Bottom and right hand . .. 103 From bottom only 2 

No fixed rule 2 

From R to L and bottom to top 1 



PRESENT PRACTICE IN DRAFTING ROOM CONVENTIONS. 303 

Q. 35. Do you always make a table to contain the bill of 
material ? 

Yes 49 No 25 Not always. . 5 

Usually 1 Use separate bill 32 

Bills on general drawings only. On details number is marked on 
piece. 

"No, but it is advisable to do so." "Have abandoned that 
system." 



INDEX. 



A 

PAGE 

A. L. A. M. Standard Screw Threads 246 

Angle, To Bisect an 19 

Angle, To Construct an 15 

Anti-friction Curve, "Schiele's " 50 

Arched Window-Opening, To Draw an •. 53 

Architectural Design 175 

Architectural Drawing 162 

Architectural Specifications 176 

Arkansas Oil-stones 5 

E 

Ball Crank Handles 263 

Baluster, To Draw a 53 

Bills of Material 292, 303 

Board, Drawing 1 

Border Lines 293 

Bow Instruments 2 

Brass, Sheet of 6 

Breaks, Conventional 61 

Brickwork 166 

Brilliant Points ic6 

Buttress Thread 235 

C 

Celluloid, Sheet of Thin ^ 

Cement Work 185 

Center Lines 60, 291 

Chains 262 

Cinquefoil Ornament, To Draw the 33 

Circle, Arc of a, To Draw a Line Tangent to an 33 

Circle, Arc of a, To Find the Center of an 32 

Circle, To Construct the Involute of a 4; 

Circle, To Draw an Arc of a, Tangent to a Straight Line and a Circle 37 

Circle, To Draw an Arc of a, Tangent to Two Circles 36 

Circle, To Draw an Arc of a, Tangent to Two Straight Lines 34 

305 



306 INDEX. 

PAGE 

Circle, To Draw a Right Line equal to Half the Circumference of a 31 

Circle, To Draw a Tangent between Two 33 

Circle, To Draw Tangents to Two 34 

Circle, To Find the Length of an x\rc of a, Approximately 47 

Circle, To Inscribe a, within a Triangle 35 

Cissoid, To Draw the 49 

Cistern 184 

Closets V. . 193 

Compass 2 

Complete Information on Pencil Drawing 290 

Connecting Rods 272 

Conventional Breaks 61 

Conventional Lines 60 

Conventional Screw-threads 62 

Conventions 56 

Conventions, Shading 104 

Cornice 190, 213 

Cotter and Gib 25 7 

Cotters ' 254 

Coupling, Friction 268 

Coupling, Stuart's Clamp 270 

Crane Hooks 264 

Cross-sections " 62 

Curves, Irregular , 3 

Cycloid, To Describe the 46 

D 

Dark Surfaces 104 

Development of a Locomotive Gusset Sheet 97 

Development of the Surface of a Cone 93 

Development of the Surface of a Cylindrical Dome 96 

Development of the Surface of a Right Cylinder 92 

Development of the Surfaces of a Hexagonal Prism 90 

Development Problems 155 

Dihedral Angles 75 

Dimensioning Drawings 297, 302 

Dimension Lines 291 

Direction, The, of the Rays of Light 105 

Directions to Students 137 

Dividers, Hair-Spring 2 

Doors 195 

Drafting-Room Conventions 289 

Drawing-board 1 

Drawing-pen 2 

Drawing to Scale 12, 54 

Drawings, S izes of Sheets 294 



INDEX. 307 

PAGE 

E 

Electric Wiring 208 

Ellipse, Given an, to Find the Axes and Foci 43 

Ellipse, To Describe an 38 

Epicycloid, To Describe an Interior 50 

Epicycloid, To Describe the 48 

Equilateral Triangle, To Construct an 24 

Examples of Working Drawings 120 

F 

Figuring and Lettering 66 

Finished Parts of Working Drawings 122 

Finish Indications 295 

Flanges, Cast Iron 291 

Floors 192 

Framing Joints 164 

G 

Geometrical Drawing 16 

Geometrical Drawing Problems 149 

Glass-paper Pencil Sharpener 4 

Gothic Letters 69 

Grade of Pencils 294 

H 

Handles, Ball Crank 263 

Hatch Lines 293 

Heating 210 

Heptagon, To Construct a 28 

Hooks, Crane 264 

Hyperbola, To Draw an 42 

Hypocycloid, To Describe the 48 

I 

Ink Eraser 4 

Inking the Pencil Drawing 290 

Ink, Red 295 

Inks 4 

Instruments 2 

Intersection Problems 156 

Intersection, The, of a Cylinder with a Cone 93 

Intersection, The, of a Plane with an Irregular Surface of Revolution 102 

Intersection, The, of Two Cylinders 96 



308 INDEX. 

PAGE 

Involute, of a Circle, To Construct the 45 

Isometrical Cube 113 

Isometrical Drawing 112 

Isometrical Drawing, Direction of the Rays of Light in 114 

Isometrical Drawing, Examples of 117 

Isometrical Drawing of a Hollow Cube 116 

Isometrical Drawing of a Two-armed Cross 115 

Isometrical Problems 158 

Isometrical Scale, The 114 

K 

Keys 249 

Keys, Fixed 25 2 

Keys, Flat 250 

Keys, Round 25 1 

Keys, Saddle 249 

Keys, Sliding Leather 253 

Keys, Sunk 250 

Keys,- Woodruff 25 3 

Key ways in Hubs 297 

Knuckle Thread 235 

L 

Lathing. 185 

Leads for Compass 13 

Lettering 137- 147, 168, 214 

Lettering and Figuring 64 

Lettering, Style of 292 

Line of Motion 60 

Line of Section 60 

Line of Shade 106 

Line, To Divide a 21 

Line, To Draw a, Parallel to Another 19 

Lines„ « 291 

M 



Machine Details 228 

Masonry Work 182 

Mechanical Drawing and Elementary Machine Design 122 

Model of the Co-ordinate Planes 8r 

Moulding, The " Apophygee " 52 

Moulding, The " Cavetto " or " Hollow " 5 r 

Moulding, The " Cyma Recta " 51 

Moulding, The " Echinus," " Quatrefoil," or " Ovolo" 52 



IXDEX. 309 

PAGE 

Moulding, The " Cyma Reversa " 52 

Moulding, The " Scotia " 51 

Moulding, The " Torus " 52 

N 

Needles 6 

Notation 8o 

Notes on Drawings 302 

Nut 240 

Nut Wrench 259 

O 

Octagon, To Construct an 28 

Orders of Architecture 171 

Orthographic Projection , 74 

Oval, To Construct an 43 

P 

Painting 202 

Paper 2 

Parabola, To Construct a 41 

Pattern Numbers 302 

Pencil 2 

Pencil Drawings 293 

Pencil Eraser 4 

Pencil, To Sharpen the 8 

Pen, Drawing 9 

Pen, To Sharpen the Drawing 10 

Pentagon, To Construct a 28 

Perpendicular. To Erect a 17 

Pipe Threads 236 

Planes of Projection, The 75 

Plastering 187 

Plumbing . . 203 

Polygon, To Construct a 26 

Porches 190 

Problems in Advanced Mechanical Drawing 277 

Problems in Geometrical Drawing 149 

Problems in Intersections i>6 

Problems in Isometrical Drawing 158 

Problems in Mechanical Drawing 134 

Projection of the Helix as Applied to Screw-threads 99 

Projection, The of Plane Surfaces 84 

Projection, The, of Solids 90 



3IO INDEX. 

PAGE 

Projection, The, of Straight Lines 82 

Projection, The, of the Cone 93 

Proportional, To Find a Mean, to Two Given Lines 31 

Proportional, To Find a Third, to Two Given Lines 31 

Proportional, To Find a Fourth, to Three Given Lines 32 

Protractor 6 

Q 

Quatrefoil, To Draw the „„.„.. 53 

R 

Rays of Light 104 

Rays, Visual 104 

Red Ink 295 

Rhomboid, To Construct the 21 

Right Angle, To Trisect a 24 

Roman Letters 67 

Roof 190 

S 

Scale Guard 6 

Scale, Drawing to . . 12, 54 

Scale on Drawings-. 300 

Scale, To Construct a 55 

Schiele's Curve, To Draw 50 

Screw-threads, Conventional 62, 239, 296 

Screw-threads, Regular 100 

Screws 228 

Section Lines 56 

Section Lines, Standard 58 

Shade Lines 297 

Shade Lines and Shading 103 

Shade, To, a Concave Cylindrical Surface no 

Shade, To, the Elevation of a Sphere 108 

Shade, To, a Right Cone no 

Shade, To, a Right Cylinder 109 

Shadows in 

Sharpen Pen, To 10 

Sharpen Pencil, To , 8 

Sheet Brass 6 

Sheet Celluloid 6 

Sheet-metal Pattern Drafting . 216 

Shingles 190 

" Sibley College " Set of Instruments 2 

" Sibley College " Set of Irregular Curves 3 



INDEX. 3 II 

PAGE 

Sketches, Freehand 287 

Source of Light 104 

Spiral, To Describe the 44 

Split Pins 248 

Sponge Rubber - 5 

Springs 260 

Square Thread 235 

Square, To Construct a 25 

Standard Screw Threads 23 2 

Stippling 100 

T 

Table, Decimal Equivalents 275 

Table, Heat Colors 275 

Table of A. L. A. M. Screw Threads 246 

Table of Chains 262 

Table of Circumferences and Areas of Circles 276 

Table of Crane Hooks 266 

Table of Flanges, Cast Iron 262 

Table of Hand Wheels 267 

Table of Shaft Collars 267 

Table of Standard Screw Threads 244 

Table of Taper Pins 249 

Table of Washers 263 

Table of Wire and Sheet-metal Gauges 274 

Tacks 5 

Taper Pins 248 

Third Dihedral Angle 75 

Tinting Brush 5 

Tinting Saucer 5 

Title, Standard 148 

Title, The, of a Working Drawing 122 

Titles 292 

Tracing Cloth 6, 301 

Trefoil, To Describe the 53 

Triangles 3 

Triangle, To Construct a 25 

Triangular Scale 3 

Triangulation 221 

T-square 2 

Type Specimens 70 

U 

United States Standard Screw Threads 232 

Use of Compasses 1 3 

Use of Dividers or Spacers. 13 



312 INDEX. 



PAGE 

Use of Drawing- tward. . ........_.... i r 

Use of Drawing-pen 9 

Use of Instruments y 

Use of Irregular Curves 14 

Use of Pencil 8 

Use of Protractor 14 

Use of Scale 12 

Use of Spring Blows 14 

Use of Triangles n 

Use of T-square . , 1 1 

V 

Visual Rays 104 

Volute, To Describe the " Ionic " 45 

W 

Washers 263 

Water-colors 5 

Water Glass 5 

Whitworth V Thread 233 

Wire Gauges 274 

Woodruff Keys 254 

Working Drawings , 118, 159 

Working Drawings, Examples of 119 

Working Drawings, Method of Making 119 

Working Drawing, What is a 119 

Wrench 259 

Writing-pen 6 



676 




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